The rule could be anything, as funny or as serious as you want. The universe will progress in a similar way that it has up until this point, unless your changed rule prevented it from doing so.
Some examples might be:
- The invention of currency is not allowed.
- Iron is slightly less stable.
- The Ancient Greeks are able to cultivate Silphium, which does not go extinct now.
You both have to solve a new (to you) calculus problem to make a baby.
OP said the universe does a hard reset. Life would never evolve if that was a new rule