Well, going by history, it's not luck, it's gambling based on historical precedence. Time and again a new technology has come along, often spurred by the problem it solved, just in time to prevent a larger problem.

The issue is that people take this for granted, and don't see it for what it is, gambling, and in this case with immensely large negatives on failure, to the point where the mental model of the world many people keep is unable to accurately assess the consequences. That's a dangerous combination.

Eventually we're going to go through some version of the "Great Filter" like wet tofu through a shredder, but this gives me hope that it won't be in our lifetimes.

Unless we already happened to go through that when life magically transitioned from monocellular, simple competitive organisms to multicellular, complex cooperative organisms...

That seems unlikely, since that transition happened multiple time along multiple pathways, and we observe that just on the single planet we know to have life.

Do you have a source for that? I was specifically speaking about the first eukaryotic cell(s).