I've used cellular automata as a thinking metaphor for how life could emerge from the Universe. If you had a large enough CA grid, starting random, you'd be guaranteed to get any possible structure. So if there are any structures that can persist and replicate, you should see them appear and start to dominate the grid.
1) This makes me think you would want a CA rule that didn't generally collapse randomness to nothingness or static structures. For example, Conway's rules on a random grid produce mostly empty space along with some bricks, blinkers, and occasional gliders. But in the Universe, even where you don't have life, you have interesting and complex stuff going on, possibly analogous to Wolfram's Rule 30.
2) In the Universe, we don't know how life started, but it seems like there might have been a fairly smooth progression of complexity. Subatomic particles, hydrogen, heavier elements, simple molecules, nucleotides, RNA, etc. This differs from the "rely on extreme luck in the midst of a flat background" vision of CA. Even something like Rule 30 that doesn't flatten everything still doesn't produce stages of increasing depth. Maybe a CA would look like the Universe if you zoomed out (spatially and temporally) 10^10 so the "extremely lucky" structures were common and interacted with each other. If so, is the enormous amount of empty space and time between structures somehow necessary?