From my understanding, yeah kinda. Will preface this by saying I’m not an astrophysicist in even the broadest sense.
But for time to exist at all, we have to assume there was a zero. And seeing as time is a measure of space, if time was zero, then space was too.
We can also ‘see’ the age of the universe. As we can see the earliest cosmic soup behind our stars, and through red shift (the way light shifts it’s wavelength over time) can calculate the age of this background to 13 billion years. So we can say the age of the universe was 13 billion years ago (relative to our viewing angle of our telescopes.)
We also know that even though that light itself took 13 billion years to reach us, The universe, and space it occupies, is expanding and we theorise that it could be as much as 89 billion light years wide. This doesn’t mean the universe is now 89 billion years old though. If you drew on a balloon and blew it up, the drawing would get bigger but there wouldnt suddenly be more ink. It’s just expanded in all directions.
We also know that space and time is affected by gravity. Space shrinks around black holes, and so does time. It’s not a clean straight line, but waves, stretches and curves as it is affected by the masses around it. From the relative positions of these black holes time and space will still appear the same and light will still travel at the same speed, it will still cross the same distance even though that distance has been compressed.
In other words from an outsider looking in it would appear that light has slowed down, and from an insider looking out it would seem that the universe outside is moving faster than it does to us on earth but this is warping nature of time and space. It doesn’t make the universe older or younger, It makes the time it took light to reach them appear different.
So for a person living in a black hole today, the red shifted light of the cosmic microwave background may look much much older, or may not have reached them yet as space has compressed, and as such the background is also further away (in raw space) and the time would be older. But thats relative to them and not ACTUALLY longer ago. Only because we’re still measuring that time scale in earth time units from our perspective in this conversation.
When I say living in a black hole I mean off the edge of the event horizon where time and space can still work according to our known principles of course!
Astrophysicists in this thread please correct me. This is a layman’s attempt at an ELI5 and is likely riddled with slight misinterpretations.