to some extent. If life hadn’t started in one particular “warm pond”, then it would have started in a different, but very similar, warm pond. Be aware also of the anthropic principle. Carbon based life did not originate on the surface of the sun because the surface of the sun is not suitable for carbon based life. The fact that we are here constrains where “here” is.
Yes. We will know how big a part when we have examined other planets for life. If, say, 25% of extrasolar planets have life then chance did not play a big role. If 0.00000025% have life then chance played a bigger role.
As far as we can tell from the very little we know about the multiverse within which the big bang happened, there are a great many bangs happening. Not all of them grow big (called “inflation”). If that is the case, then the bang was necessary while the big was probably not. Again, they depends on what proportion of bangs get to be big.
For a look at some fairly recent thoughts on cosmology read
“the myth of the beginning of time”.
Rossum