It's the same as how current simulations work in the engineering world today. You load up some boundary conditions, press solve, and the machine spits out stress/strain, fluid motion/thermal capacity, SI/PI whatever the study was for.
So you need the equations, constants, and variables from the start of the big bang, press solve, and the simulation works everything else out. With an accurate enough solver model, it will process the exact quantum effects at every moment until it reaches the current day.
If you want to account for the multiple worlds theory which means an individual simulation for every possible quantum choice then sure - it will take a lot longer but it would still be possible. The bulk of the simulations would be discarded when they veered away from plausibly becoming the representation of the universe we currently live in, so the AI would not have to juggle infinite simulations at the same time.
On the other hand, if we as humans have carefully recorded our universe as it is, with whatever degree of accuracy needed, then the AI can start from that point instead of the big bang. It might not even have to be accurate, it may be able to interpolate data very accurately (much like RTX does with ray tracing).
So given sufficient AI intelligence, power, and time, an AI could simulate our exact existence. And that then proves another theory - simulation theory. If our AI can simulate atom for atom, then the chances that we ourselves are living in a simulation becomes extremely high.