> the thousands of years I could be a human, I wind up in this time?

It can be continued. The decades I could ponder those questions. The minutes I could observe this date and time on a calendar. And so on. Reference class problem.

Going the other direction, if you disentangle consciousness from everything that links it to whatever you observe now, it would be equally present in every conscious being, so the question "why it is present in me?" loses surprise. It is present wherever whenever, so in me too, no biggie.