I have an OBS recording but I don't know how to setup a timer, I wonder if I can submit my run without a timer.

Generally yes, but some leaderboards do require having a timer in their rules, so be sure to check the rules for each game you run.

As hahhah said it depends on the rules of the game.

If the game has a built-in timer (like in a racing game) you're almost sure to be all good.