A good contribution.
My response is that, as far as we know, space and time are not infinite. We can measure the distance to the cosmic background microwave radiation (CMB), which is presumed to be the limit of the observable universe. According to theoretical physics the CMB represents 400,000 years after the big bang, when photons were able to freely move through the universe.
That places constraints on the size and age of the universe.
13.8 billion years is still a lot if time for biological evolution to occur in the cosmos, if it did.
I keep coming back to the wierd fact that life only evolved once on earth. Every living thing today is a genetic descendent of the first microbes of 3.8 billion years ago. The earth had been around more than 4 billion years, that is almost a third of the age of the universe. If we assume life is so cosmically ubiquitous and resilient, why did life only evolve one time on earth? Why are we not seeing multiple evolutionary events of exotic life forms and life forms of an entirely different genetic heritage?
To me, it either means the evolution of life is an exceedingly rare event; or DNA-based life is the only realistically possible form of life; or maybe ancient Earth did have multiple evolutionary events but we have just not seen the evidence.