Sure. Here is one way to estimate the statistical probability of the Big Bang occurring without an external mover.

We can start by assuming that the initial state of the universe was completely random. This means that the probability of any particular state occurring is equal to 1/(number of possible states).

The number of possible states is incredibly large. For example, if we assume that the universe is a 3-dimensional space, then there are 10^80 possible states.

This means that the probability of the universe randomly assuming a state that is consistent with the observed expansion is incredibly low. In fact, it is so low that it is essentially impossible.

This suggests that the Big Bang required an external mover. However, it is important to note that this is just an estimate. The actual probability of the Big Bang occurring without an external mover could be higher or lower.
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