When even the Likelihood function is intractable to compute.., but the model can be (stochastically) simulated. Similar regime as for Probabilistic programming?

In ABC, we simulate the system with different values of the parameters (sampled from prior), and compute some summary Statistics. If the summary statistic is close enough to that of the observed data, we accept that run, and save the parameter values that generated it.

We end up with a sample of parameter values which is our approximate posterior.

There are more advanced variants: sequential particle MC...