Yes, well, of course, "infinite" DOES make it not only possible, but inevitable. ....But what about this: If a number of monkeys equal to the total number of particles in the universe typed furiously at the rate of a million key-strokes per second for 5 billion years, would their be enough information to equal that in the most simple self-sustaining cell known?
Just for starters, something on the simple side: how are you going to get sufficient lipids for your cellular bi-layer, all appearing in the same restricted physical space, all at the same time, from non-biological sources?
See, I can't even get paragraphs right without harmful mutattions.
if it were infinite one would get it on his first try.