For example, was there a July 19, 3110 BC? Will there be a July 19, 3110 AD for sure, or is it dependent on the continued existence of the Gregorian calendar / humanity / planet Earth?
Calendars represent an arbitrary period of time. If humanity ends before that date, it won’t exist other than as just another solar day, assuming the earth is still around and spinning on its axis that is.
The correct answer is, this depends on the definition of the calendar: e.g., months in the Arabic calendar start depending on actual eyeball observation of the Moon.
If you want to know whether it is useful to use the Gregorian calendar to describe events in the Bronze Age, not really. It is also not very useful thousands of years in the future.
There was a period x number of days before the present, that can be converted into a calendar date. Which calendar you use is arbitrary but why not put it into a familiar system? Such as call it “October 30th 1207 BC” instead of “the third year after that weird cow did the thing” like some contemporary scrap of papyrus might call it?
Said another way …
The calendar (whichever you prefer of the dozens on offer) depends on humans.
The existence of a moment in time (or ~24-hour period of time) on Earth does not depend on humans. It doesn’t even depend on the existence of Earth. If in the far-flung future some contingent of humans (or successor organisms) lived on some other planet orbiting some other star, they could still (in principle) compute an earth date according to an earth calendar even long after the Sun had engulfed the Earth and converted it into a cloud of loose atoms and ions.
Agreed. If humanity does survive what to me seems an inevitable apocalypse, then the apocalypse will probably be considered year zero, and it will then count up from that point.
This is a variant of the philosophical discussion of whether math/numbers/particles/reality exists outside of humanity. I’m on the side that says yes.
So there was a July 19, 3110 BCE. Also a 3110000 BCE and a 3110000000 BCE. Similarly there will be a July 19, 3110 CE. Also a 3110000 CE and a 3110000000 CE whether or not humans survive or the Earth, for that matter.
Another way of looking at the same POV …
Once I create a ruler I can use it to measure anything, even something far away.
None of us doubt that the average diameter of Pluto is some specific number of feet. Or of meters. Nor do we deny that the conversion factor between feet and meters here on Earth today is the same as it is on Pluto today or tomorrow even though we’re not there to measure it.
A calendar (or a clock) is a ruler for time. (setting aside Einsteinian relativity issues for a minute). And as such can be used to measure time whether or not we’re currently experiencing the moment or interval being measured. We can use it to measure time at a great distance from current time. Such as the dates @Exapno_Mapcase used for his examples.
How would you account for years that had a different number of days in it. Not Leap Years, those can be accounted for. But rather when the Earth rotated faster so there were more days in a trip around the Sun?
Nobody said it would be easy.
Astronomers have issues now calculating time on other planets. Mars has a year of 687 earth-days of 24.5 earth-hours. If we had evolved there our calendars would like entirely different.
Nevertheless, there’s a period on Mars that will correspond to the 24 hours that we currently call July 19, 3110 CE. Here’s a converter.
That humans have difficulties applying their arbitrary metrics to other places or times is a limitation on us. There’s currently not much need for day-level precision for dates three billion years ago. I’m sure if there were, people would work on the problem and solve it. For our purposes. The universe doesn’t care.
In addition to all those good points made by @Exapno_Mapcase just above …
The very term “Day” is complicated on Earth. Would those be apparent solar days, mean solar days, civil days, or sidereal days? Earth has all 4 kinds every day, including today.
Timekeeping and calendaring are one of those topics that seems kinda straightforward until you look just a wee bit more closely then it violently explodes into a cacophony of complications. See here for a bare intro:
Basically my thought, too.
Does 15.24956 billion kilometers “exist”? With or without humans it certainly does. It’s just the units that indicates human involvement.
This is a more complex question than it first appears I think.
If you just extend the Gregorian Calendar back, for example, would Caesar’s assassination have taken place on the 15th day of March, 44 BC? I’m not so sure, since the rules for leap years and such have changed over time.
So we have to decide what to do about that. Do you take the Gregorian Calendar all the way back to a billion years ago?
Also, the length of the day changed when you go back far enough, so that complicates things too…
You would be looking backwards in increments of modern 24 hour days and 365.25ish day years. The length of day back then wouldn’t matter. (Is it day or night on Tuesday, January 4th, 500,000,002 BC? It is both, just like it is right now. The location of the sun on that day matters only when you are specifying a specific spot on the planet at a specific hour, which introduces a whole new question–is the “spot” defined by modern map coordinates or by the piece of land? Then you would have to account for keeping track of continental drift.)
I’m also on the side that says yes to that particular question, my brother. 
It’s hard to imagine a world where discrete objects that can be counted don’t exist. And once you have the counting numbers, the rest of our mathematics follows.
But this is slightly different, because the number of Earth days in an Earth year can change over time, quite possibly by enough that having 97 leap days every 400 years isn’t the proper correction if one goes sufficiently far back or forward in time.
Even without any change in the ratio of days to years, 365 + 97/400 days per year is sufficiently inexact that we’ll eventually need to make an adjustment - IIRC, we’ll need one less leap day sometime in the 5th millennium CE. If man is still alive, etc.
Since the whole point of going from the Julian to the Gregorian calendar was to keep the calendar from getting out of synch with the seasons, my take is that the Gregorian calendar becomes inaccurate when it in turn gets out of synch with the planet, so referring to times on Earth by Gregorian dates more than a few millennia forward or backward in time is inaccurate.
Everything you have said is true.
ETA: Same to @RTFirefly just above.
But is IMO irrelevant. Effectively you’re talking about a units conversion problem. How many meters in 1,234.56 feet? How many 2024CE days in one 100,000BC day? Which Gregorian date corresponds to [this] Hebrew / Chinese / Mayan / Julian date? All those questions are the exact same idea.
Now admittedly the specific details of gathering the info necessary to perform a date calculation in the face of a changing planetary orbit and planetary rotation rate will be harder than multiplying by 0.3048. And, as I noted upthread, has to begin by deciding which of the many flavors of “day” we’re interested in.
Converting between various modern and historical calendars which may have had arbitrary resets or adjustments. It’s just more of the same.
And none of which bears on the OP’s underlying philosophical question of whether time exists absent humans to watch it.
I guess I should have finished up that thought - that the Gregorian calendar was designed to keep as constant a relationship as possible between its dates and Earth seasons, e.g. equinoxes and solstices should continue to show up at the same dates on the calendar. Whether or not we’re still around to observe it.
So from that standpoint, it is a misnomer to talk about November 14, CE 52024, since extension of the Gregorian calendar to then would have the summer solstice happening around that date, if my back-of-the-envelope calculations are correct.
I can understand the utility in certain fields of using some variation of the Gregorian calendar as a way of saying when certain things did happen or will happen. But for instance, saying an eclipse happened on October 30, 1207 BCE, what does that mean unless Egyptian records of the time are exact enough to allow us to put other events at fairly precise dates on that same calendar.
If we can say, for instance, that Pharoah Soandso took the throne on July 17, 1198 BCE, then the ability of historians to refer to dates of events on that calendar has practical meaning. But if the eclipse is the only thing the historians can date because the records aren’t precise enough to say how many days before or after this eclipse any other events happened, then it’s really pretty useless for the historian. And for the layman, the month and day (probably about a day off anyway, that far back) doesn’t add any more meaning than saying ‘the fall of 1207 BCE.’
One problem is that January 1 is arbitrary as the first day of the year. If the first day were based on the Sun-Earth relationship like the vernal equinox or winter solstice it might be easier but even then the precession of the equinoxes and changing tilt of the axis would still present problems
We keep poking at the problem of metrics and measurements. That is a problem precisely because we have devised a set of tools, some physical, some mathematical, applicable almost solely for local usage. Local meaning our Earth time and Earth space.
Calendars date back as least as far as Göbekli Tepe 12,000 years ago. Their measurement stick was a day, either sunrise to sunrise or noon to noon. A year provided more difficul, and needed precise and long-term understanding of the sun’s place in the ecliptic. With those, intermediate points were determinable, such as the period from full moon to full moon, the start of seasons, and the proper date to celebrate religious fests like Passover and Easter.
Those metrics famously fail when they tried to be applied elsewhere. Star Trek locked that fail into popular culture when it needed to invent the “star date” to account for the ship’s unearthly movements. Star dates were a sort of universal translator, not conceptually different from the way historians try to convert historic amounts of money into today’s dollars to make the terms relatable. Doing so has innumerable problems, not least that a book I read in college will use “modern” figures that are ludicrously low today. History need not come into it: try calculating the day-by-day or even hour-by-hour buying power of a currency in hyperinflation by using dollars.
My point is that those of us who are not immersed deeply into the scientific and technical world are hopelessly attached to the familiar, and seek to apply familiar measurements far past the quotidian points for which they were devised. Using a meter stick to measure a protozoan will give no results, although nothing is inherently wrong with either the stick or the one-celled creature.
Measurement is a critical piece of understanding. If humans have no tools by which to measure a thing, we often lack basic understanding of what that thing is. Consciousness is stymied by this lack. Intelligence has been misapplied by multiple flawed attempts at measurement. In the physical realm, the effects of what is called dark matter can be measured but they give no clue as to what thing or things the matter is, leading some to doubt its very existence.
Again, I’m arguing that human limitations are at base the source of measurement problems. I’d also argue - fiercely - that the breadth and scope and precision of the measurements we have been able to devise are breathtaking, one of the greatest achievements of human history, perhaps surpassing controlling fire and the wheel. That we have more work to do is trivially true, because it true for all human endeavors. Language is our other greatest tool; discussing the work to come is part of the same game.
October 10th, 1582 never existed in the Gregorian calendar by definition. It still existed in the Julian calendar though. I would say calendar dates refer to days defined in that calendar, not just the time the consumed during any particular revolution of Earth or any other definition of a day. So 10/10/1582 only existed for some people and not for others. Of course you can define any calendar you want to include any day you want by any name, including nonsense calendars. Days happen, just like sands through the hourglass. Dates not so much.