We could artificially create a sterile, large pool of the ingredients and see what happens.

I've read about experiments like this but only at lab beaker scale.

I don't think you'd want a single homogeneous "large pool", but rather a large variety of different types of micro-environment, including all those that have been suggested as possible environments for the emergence of life - the chemical and physical environments of hydrothermal vents, volcanic hot springs, shorelines, different types of rocks, clays, etc. You'd want to have environments that included all energy sources present on earth (solar, lightening, geothermal), all forms of mechanical agitation/mixing (hydrothermal, waves), etc, etc.

The bigger the pool the harder to create it here on Earth without introducing problems. For example, take a prion. Hard as hell to actually get rid of, how do you know you've not actually introduced something like this to your sterile pool that's going to make it do things you don't expect.

Yeah, but it seems impossible to experiment on the scale that would have happened in nature where there would have been millions of localized "test tube experiments" ongoing for millions of years.

Of course people can, and do, try to replicate early earth environments and self-assembling proto-cells, but I'm not sure how intellectually satisfying any self-replication success from these "designer experiments" would be, unless perhaps done on such a large scale (simulation vs test tube?) that any conclusions could be made about what likely happened in nature - just how specific do the conditions need to be?

The biology equivalent of "infinite monkeys at a typewriter"

It's funny talking about non software stuff on HN. I'm sure there's hundreds of papers on simulations and expert analysis of this.

Does 'we' include 'you'?