A good observational/ amatuer astronomer could probably do it. They could do it easy if they had just a small telescope and some reference books.
If they were the type that can remember some basic critical numbers/info, they might not even need the books, but they would have to do some calculations to recreate the reference book.
If they were really good, they might not even need the telescope or the books, but they would have to be pretty good.
I’d be fucked.
I could probably determine the continent from whatever animal was eating me.
Probably the best I could do is tell you that it wasn’t where I come from - not a South Carolina pine forest or a Lowcountry swamp or the Appalachians.
Latitude, yes. Anything else, no. As noted, the difference between the middle of nowhere Canada and the middle of nowhereski Russia are minimal in the extreme.
An observation. Many folks are saying they can know where they are based on observations of geographic features, flora, fauna, climate…
And I have little doubt that is doable.
But here is the problem. Does being saved require you being able to say " I am a few hundred miles west of Mt Middle of Nowhere"? Or does being saved require you to say
“I am at latitude abc, longitude xyz, plus or minus 500 miles”?
Being able to do the second from these kinds of observations requires you to at least have a decent globe or set of maps. Or a pretty darn good mental image of them.
Its the difference between knowing where you are and knowing where you are and where the where actually is.
This Globe Genie site might be a good way to practice a bit. Uncheck “Current Location” and click “Teleport.” It will put you on a random road somewhere in the world. I have fun trying to figure out where I am.
The North Star always seems stationary, no matter where you are on the planet. If it were directly overhead, you would be at the north pole.
Latitude can be identified from the angle of the North Star above the horizon. One could fashion a simple inclinometer from items in the natural world (per the OP’s problem statement) and estimate that angle, probably to within ± a couple of degrees. One degree of latitude is about 70 miles, so now we’d have latitude pinned down to within ±140 miles.
If you find that your latitude is greater than 76 degrees, you are within 1000 miles of one of the poles, and you now know your location to within a couple thousand miles, regardless of longitude.
Longitude is much harder. The observable nighttime constellations depend on season, so knowing them wouldn’t help you ID your longitude. You’d have to rely on local geography/geology and ecology. In most cases, it is at this point that I’d be screwed.
Uh yeah, much better stated that way.
Shame that as soon as you move the cursor it tells you where you are otherwise it could be fun. 
How they gonna do this without a clock referenced to UTC?
I could tell lattitude, and I might recognize distinctive fauna (esp megafauna) so I’d have a chance at guessing my continent correctly but that’s about it.
I would just sit quietly and wait for spammers to find me. They would then tell me where I was.
I’d be a dead man. I need my GPS to find my way from my living room to my kitchen.
A simple example would a lunar eclipse. When it starts is independent of where you are on the earth. IF you have the reference info, or recalculate it you know what UTC/GMT time is.
Not the most practical example but it gives the general idea.
A close planetary conjunction might pin what time it is down to the hour (which is about the precision the OP requires). But you’d have to work at it and probably build yourself a crude sextant. Or a planet passing near a given star. Or the moon grazing past a given star (but that would require some extra corrections because thats kind of a chicken and egg math problem).
If you have a small telescope, you can easily observe Jupiters moons and figure out the time in short order with the right info.
With the same telescope, you could probably do the same observing one of the brighter faster moving asteroids.
Some variable stars are also useful time keeping “devices”.
Most serious/experiences astronomers could not do this on the fly. They would fail the test. But, if you forwarned em and gave em some time to prepare before you dropped em off, the better ones IMO would have a chance.
Considering I can only identify a handful of constellations, I too would probably only be clued in by the animals in the area. Unless there were cactus or palm trees, my limited knowledge of botany wouldn’t help much either.
Depends on where I was dumped. If there were kangaroos jumping around, somewhere in Australia would be obvious. Then if I had to rum from a crocodile chasing me, narrows it down further. And if I were drowned in flooding, even closer.
According to the OP you don’t know what day or season it is; wouldn’t most of these methods require knowing more or less what day it is?
And, am I correct that knowing current GMT at some point only gets you your longitude if you can compare that with local time – requireing a clock that can keep track of time between your GMT observation and local noon? Sure, if you’ve got a telescope you’ve probably got a watch, but wanted to be complete. The clock would also probably be necessary to time sunrise and sunset if we’re figuring out time of year from that.
If you know your latitude, you can determine the season with a reasonably-accurate clock by measuring the duration of the daylight. Could I build a water clock accurate enough to determine that? I don’t know, but I could give it a shot.
All of this requires either the reference material to look up things like sunlight duration during different days at latitude X, or a lot of pencils, paper, and time.
I wish I knew the stars well enough to locate myself just by looking carefully at the night sky. I sort of feel like a smart resident of the planet ought to know his way around on that basis. But I don’t. I only know a few constellations, and wouldn’t know how to properly interpret their positions (beyond finding north if Polaris is in the sky) even if I spotted them.
On the other hand, I think I’m sufficiently versed in climate, topography, flora and fauna, that I could place myself to at least the correct continent, and in many cases the correct quarter-continent.