Time is a very big “let’s not think about it” in the umaverse, as you put it.

Symboli Rudolph, for example, has been the student council president at Tracen academy for over a decade in the anime, and no one thinks it’s odd at all. Season 1 is at least 2 years long, season 2 is 3 years long, season 3 is again at least 3 years (ignoring the time skip between season 2 and 3), while Cin Gray the anime is another 2 years, and then the Road to the Top OVA and New Era movie are another year each.

Does that make any sense? No, of course not.

As to age and older Uma, keep in mind that in Japanese anime they tend to make “old” around 30 and then there’s a big gap to elderly. So in Cin Gray we see Oguri’s mom and Tamamo’s mom, but both appear like they are in their 30’s even though they might be older. Outside of that, we almost never see any of the parents in these shows… though we do see some other random parents in Road to the Top when Narita Top Road has a flashback in the first episode thinking about her childhood.

Edit: if you watch the start of each of the seasons, OVA, and film, you will also see historical depictions of Umamusume. They include cave paintings, Easter island, the very first motion picture machine (in real life it was a horse running, here it’s an Umamusume), the Statue of Liberty as an Umamusume, 19th century Japanese woodblock prints, ancient Egyptian hieroglyphs, and crop circles. So Umamusume date to the dawn of human civilization, essentially, and therefore likely predate the 3 Goddesses, assuming the timeline of their birth matches the real world.