> That could also mean life has to get started early or it won’t at all.

How would that work? It seems to me the only that matters is that the proper conditions for abiogenesis be maintained for whatever duration it requires. It shouldn't matter how far along the Universe or planet history this period occurs

If life gets started in the violent conditions of primordial ocean in contact with primordial crust then there could be any number of factors that change that drastically lower the probability of abiogenesis happening. Like a change in the chemical makeup of the primordial ocean or crust or both. It could be the depletion or accumulation of any number of chemicals that interfere with or are needed for abiogenesis. My money would be on self catalytic reactions that use up the ingredients for abiogenesis being common in environments suitable for abiogenesis. Life could be rare because when you strike a match you should expect fire not some slow burning reaction that persistently stores information in a way that learns and if you get the fire you don’t get the life because they burn the same materials. If that is the case then life would need to be extremely lucky to exist long enough to evolve to the point where it has diversified its energy and material inputs past the point where it would be stopped in its tracks by simpler competing reactions that are closer to fire than life. I like this possibility more than simple environmental change because it makes the Ferny paradox far weirder of a calculation. Water worlds in the habitable zone for example would end up being mysteriously devoid of life since they would be perfect for non life reactions to take over where as planets with many isolated environments like lakes and tide pools could have a higher chance of recycled chemicals broken down not immediately being contaminated.