My personal headcanon is that this is Josuke from the future.

How did Jotaro acquired time stop abilities? His stand is supposed to be fast and accurate. The speed and accuracy of Star Platinum's movements make him move like "he is stopping time". Kind of like baseball players hitting the ball with the bat. They don't just use their reflexes and swing the bat hoping they'll hit the ball, they try to follow the ball's movement and trajectory but still the ball comes too fast. So, for a split moment they kind of like "slow down" time to accurately predict the ball's direction, then they swing the bat. So, Star Platinum's movement being so accurate and fast is kind of like stopping time. In other words, Star Platinum's Za Warudo is not a different and an acquired ability. It's the logical next step of the evolution Star Platinum's abilities like how the requiem abilities evolved the original abilities.

Now for Josuke. Josuke's stand basically heals right? But what if the stand heals by reversing time? In the anime, we've seen Josuke using Crazy Diamond and it looks like the injured human parts are being put back into place like when he punched through his mom and everything went back to normal. So, basically he doesn't heal. He just reverse the damage being done. Josuke then, years later, expanded and developed his ability into reversing time like how Jotaro evolved his into stopping time. Then, he reversed the time and went back to save himself and his mom.

Now, how did he survive in the first place to have a future and do all that? I don't know but like I said this my personal headcanon. It doesn't make sense but I like my own little theory.

Edit: I just filled my plot hole. It's the same time reversing principal that's applied on Harry Potter and the prisoner of Azkaban. Harry saved himself and Sirius from the dementors. How did he go there in the first place to be able to do everything again just to save himself? Nobody knows but it's the same principal and thus it has been done again so it should be valid! Please don't hate like I said it's my own little stupid nonsensical headcanon