Your understanding and proportional mistakes are breathtaking. For this earth to be an accident is roughly the same odds that a tornado goes thru a junkyard and assembles a functional Boeing 747, complete with meal service and drinks. There is not enough time for that to EVER happen by accident.
Your lottery analogy is so mathematically insufficient as to be absurd.
Lottery is just a tiny example of people not comprehending probability in large numbers. Infinity even dwarfs the probability of finding one atom in one grain of sand on the entire planet.
I think the earth is far more rare than the 747 event but both are possible *IF* the Universe and time is proven to be infinite (or close to it).
I believe in some type of creation at a higher level but believe our physical realm will eventually appear to be pure randomness from our limited perspective. Some will say the events are evidence of intelligent intervention while some will say they are pure random chance. There will be no way to prove either way and it will show that our understanding of reality beyond our limited perspective is nothing but faith.