This means that, in order to win the 'lottery' of life, you need more than the atoms in the observable universe. A LOT more.
At any one time, yes. When you have millions of years to work with that acts as a multiplier on "lottery tickets" as well---a fairly large one.
Our ability to design a self-replicating molecule is irrelevant; there are lots of things nature does better than our designs.
I'm also going to question your conclusion that evolutionary forces are irrelevant. Certainly, it wouldn't work in the traditional sense. However, it's possible that certain molecules had advantages (or disadvantages!) of some sort given a particular environment, and this could prune the decision tree considerably.
I'm not saying it's not unlikely, mind.