LUCA, the "last universal common ancestor" of all living organisms, lived 4.32–4.52 billion years ago, according to a study from NIOZ biologists Tara Mahendrarajah and senior author Anja Spang, with collaborating partners from Universities in Bristol, Hungary, and Tokyo. Their research is published in Nature Communications.
Not really, from what I understand, it seems that life just needed a match start with the right amount of momentum in a place where the building blocks were present in abundance. There might have been false starts to life, more than once. I think the rare thing is more for the right conditions (in addition to and especially in relation to the energy source: sun) to be present for the match to spark and then the conditions must be stable enough for the momentum to keep up, like a tornado.
https://www.smithsonianmag.com/smart-news/building-blocks-of-life-found-on-samples-collected-from-an-asteroid-180980231/
Tldr sperm gets shot everywhere, but the fertile eggs are rare.