As time is part of the 4 dimensional Minkowski space, saying that the future, past and present don’t coexist would be like saying left doesn’t exists when you’re going right.
Not in any way that is inconsistent with an evolving universe, actually. Sure, an observer may exist at some coordinates in 4D spacetime where they are detecting light from Sagittarius A that in our frame is 1000 years old, but also light from the Sun that in our frame is 1000 years from now. But that observer cannot be meaningfully said to be either in our present nor in our past. And if we ever "meet" to discuss our observarions, it is guaranteed that it will be no less than 1000 years from now, after we also see the sun evolving. We'll essentially only disagree about how old the light from Sagittarius A was.
Most importantly, SR is not consistent with any ordering of events that breaks causality. If I drop a mug and it shatters, no observer can see the mug shatter and then see me dropping it. So, there is no reason to believe that the shattered mug already existed somewhere in space time when I dropped it, though there is also no reason to believe that it didn't.
The result is that some reference frames have other frames future and past events, so to the grandparent posts point, there is a real sense in which the future exists along with the past. No reference frame gets to say what the official “future” is, so it must already exist.
Additionally, there are events that are in the future for any observer in any reference frame anywhere in the universe (except for those already caught beyond the event horizon of a black hole, but their future consists exclusively of the black hole so it's not that interesting to the discussion). For a simple example, present day on Earth was in the future for any observer anywhere in the universe 5 seconds after the big bang, regardless of their speed. So, there is no reason to say that present day Earth must have already existed 5 seconds after the Big Bang.
Of course, the block universe model is self-consistent, so it's possible it's correct. All I'm claiming is that an evolving universe is also consistent with relativity, though the way it evolves is more complex than a single universal arrow of time.
Every possible observer has a clear view of their own past and their own future. As long as two observers are a long distance from each other, they may disagree on the order in which events that happen far away from each of them happen.
But, they will never disagree on the order in which events that are close to either of them happened. And, if they ever meet, they will have a shared notion of what is in the past and what is in the future compared to the moment of their meeting (that is, any event that is in the future compared to their meeting for one of them is also in the future after their meeting for the other).