Simulation of Miller-Urey experience
Theoretically you can simulate any reaction an a computer, provided it is big enough of course.

Practically however, this should be close to impossible. Here are some thoughts on how to approach that and their related problems.

First, one would have to model a complex reaction mixture including the educts $\ce{H2O}$, $\ce{CH4}$, $\ce{NH3}$, and $\ce{H2}$. Simulating those alone, without considering reactions, should be possible using molecular mechanics. This should scale up to a couple of thousands of these simple molecules.

Modelling all the possible reactions requires quantum mechanical approaches. But this does not scale anywhere close to macroscopic quantities.

One could model all the individual possible reactions one at a time. Then it is possible to compare how fast they are and how much energy is required. From that one could deduce how likely a certain reaction is, and feed this into the molecular mechanics calculation mentioned above.

First one would have to figure out all possible product of the reaction mixture, including all intermediates. This alone should yield a huge number of candidate compounds. But maybe one could try to focus just on a single product and one path there. Based on experimental results, pick a target compound of interest and a possible reaction path/mechanism. Experiments should give information on both, products and intermediates.

But even simulating a predefined reaction path (i.e. the educts, intermediates and final product) is a challenge. Different relative positions of the atoms in a reaction need to be considered (the energy landscape along the reaction coordinate). Ab initio molecular dynamics (AIMD) is an approach to do that. But there are still a number of approximations involved. This is costly and of limited accuracy.

We also need to consider the spark from the electrodes. This will lead to electronically excited state and ionic intermediates. This adds quite a lot of complexity to the already difficult task.

In summary, tackling the whole thing at once is impossible. One would have to break it down into many small steps, maybe then it becomes feasible to focus only on very specific aspects.