I mean, it's not actually infinite though, neither in combination or in observable space. There are very particualar conditions required for life, and as time goes on and we approach heat death other instances of life coming about become less and less feasible.

We barely even made it ourselves. The ice ages nearly wiped everything out, and there was a time before animals where the plants nearly choked on the hyperoxygenated ready-to-burst-into-flames-any-second atmosphere, and the animals came around to respire just in time.

There are a profoundly large number of variables required for life, and I think the number is probably higher than people think. So I think it's very unlikely there have been many, if any, other living species in the universe. Moreover, if any have ever existed, I would wager they'd have killed themselves off by now. I mean, we're not doing spectacularly ourselves, I doubt we'll last over 10,000 more years. There's a very small window in which life exists, and if life is as rare as it seems, it's even more unlikely there'd be an overlap between two species in the 4 billion years or so they have to live on different ends of the universe, and even more unlikely again that one of the species in the overlap would be one on earth, and more unlikely still it would be us humans.