For a single bacteria cell, our timeframes must seem immense too.
I’m not saying it’s particularly likely, but it’s a trap to think that just because you can’t fathom the scales that makes it impossible. The universe is huge and very very old. It can afford to wait what is a long time to us for something to happen.
I do think you’re likely right in practice though, and that it is too long for the universe to be an organism. But who knows. We already know that mathematically speaking the heat death of the universe looks identical to a very zoomed in big bang, maybe we just need to zoom out a few billion orders of magnitude to see the big picture, where the vast distances and time scales we see appear as little more than micrometers and microseconds apart…
The scales involved are vastly different than the minor difference in scales between bacteria and us - we don't have to worry about the speed of light for anything that we currently consider alive.
Unless there's something big we're missing. Maybe the cores of stars contain the final ingredient required for DNA formation or something.