Can an infinite universe explain the Fermi Paradox? Explanation of potential problem:

We're not completely sure exactly how unlikely an event Abiogenesis was, given both the extreme unlikelihood of nucleotides randomly assembling into anything making sense and the vastness of primordial ocean and extent of time it existed. And still, despite their vastness, when involved with probabilistic chain of events we're quickly getting numbers by which planetary scale pales.

It may very well be that the event was unlikely enough to be nearly impossible not only on the planetary scale, but even on the galactic scale - or even on scale of the observable universe.

My proposed solution to this problem:

Regardless, with the actual universe being infinite, it would be bound to happen somewhere. Still, occurrences of life could be separated by many times the width of observable universe, and none of them could ever contact another.

...which would offer a possible explanation to the Fermi Paradox.

Does my proposed solution address the problem I outlined above, or is there a flaw in my reasoning/understanding?
The true explanation to the Fermi paradox is not known. There is a very long list of proposed explanations, some of which are listed here:

https://en.wikipedia.org/wiki/Fermi_paradox#Hypothetical_explanations_for_the_paradox

What you're saying is literally the first one on the list, also known as the Rare Earth hypothesis.

https://en.wikipedia.org/wiki/Rare_Earth_hypothesis