First of all, the scientific community's current answer is EXACTLY that; current. It's ever-changing. That's one of the most beautiful things about science, it doesn't rely or beg acceptance upon age-old doctrine to stay relative. Change, if anything, is the more natural force.
And sure, the chances of life JUST HAPPENING are astronomical. That's why, and the theory stipulates, we're one of very few in this quadrant of the galaxy...or the universe, with life consciousness. Water, and therefore the possibility of life was discovered on Mars, true. A very primitive form. Something that may dictate a past that some millions of years ago held more advanced forms of life...not necessarily consciousness. Fact is, our planet was the Goldilocks of the Cosmos. It was just right. It's not a miracle. It wasn't by choice. It's the game of odds. We, as humans with no full understanding, simply place significance on it.
The only time infinity comes in to play for scientists is in the very small, the very large, or the one theory of the recurring big bangs. Time isn't relative. But if you'd like to look at time, one might consider the 3 million year old Australopithecus fossil of Lucy. Now...this is obviously up to you to believe or not, but consider the time involved if you do. In 3 million years, Australopithecus evolved into us. 65 million years ago, which is how long Australopithecus would take to evolve into YOU and ME 21+ times, brought us the dinosaurs. Proto-amphibians (fish) appeared some 500+ million years ago. All of this, still a FAR cry from 1 billion years. And the earth has supposedly been around for 4.5 billion. You speak of an infinite amount of time. Life doesn't need it to evolve. We've only been involved in heavy industry for a little over 200 years. Who knows where our understanding will extend to with 10,000 more?