As made clear above, there isn’t any special case that could be considered standard. If there could be an exception, it might be the “average speed of everything in the universe”. Sadly, there isn’t any such average. Everything is pretty much moving away from everything else, so you could pick any one of them and it would appear to be the average (everything moving away, at the same rate for a given distance, things farther out moving faster).
There isn’t any good candidate for a standard reference for time, other than wherever someone is making measurements. Even here on Earth, there’s no standard reference, when discussing very small timescales (where the differences due to local variations in gravity and due to the Earth’s rotation are significant enough to matter).
Just as there isn’t any standard for duration of time, there’s no good standard for a point in time, or whether to call to events “simultaneous” or not. That is, if events A and B are close enough in time (and far enough in distance), observers going different speeds will report whether A happened first or B happened first differently. (That "close enough in time " and “far enough in distance” are set by whether there was enough time for a beam of light to get from one to the other. If there was, everyone will report the same sequence of events.)
But there is an objective reality that all can agree on. Imagine that spacetime is like a loaf of raisin bread. Time is on the long axis, and space (only 2D in this mental image) is like a cross-section of the bread, if we were to slice it. Events at locations are raisins in the bread. Let’s set up our units so that if event A at location a sends a beam of light to location b causing event B. the beam of light would take a 45-degree angle to the time dimension (the length of the bread). So, the line from raisin A to raisin B is 45 degrees off the longitudinal axis.
Now, we baked our loaf of bread based on our own observational frame, so if we slice the bread at 90 degrees, that’s the universe at one point in time. If we see raisins C and D in our slice, we’d call those simultaneous. But, someone moving from the front of the loaf to the back would see things differently; their “simultaneous slice” would be at an angle to ours (looking from above). Based on their slice, C and D would be in different halves of the loaf: one in their future, one in their past.
So, same objective reality, but different viewpoints cause different observations. No slice can be greater than 45 degrees. But is the 90 degree slice special? No, because that other observer would bake the same loaf a bit differently; it’d look stretched to us, so that now WE would have to cut at an angle to show our slice of simultaneity.
My thanks to Brian Greene for the image, my apologies for butchering it. Or half-baking it, to avoid mixing metaphors.