Also not very educated on this, but just throwing out what i thought was the outline here:

1. Tiny differences in position or speed can lead to drastically different outcomes https://en.m.wikipedia.org/wiki/Chaos_theory
2. We can only know position or speed https://en.m.wikipedia.org/wiki/Uncertainty_principle Thus, predicting the future cannot reach 100% accuracy.

If this means that we might have free will i cant say, but if the world is wholly deterministic, the above at least underlines our lack of ability to predict it.

Regarding god of the gaps, annoyingly, the claim here is actually that we ”know” that we cant know:

”Thus, the uncertainty principle actually states a fundamental property of quantum systems and is not a statement about the observational success of current technology.”

Of course, only until falsified - field is always changing: https://www.scientificamerican.com/article/common-interpretation-of-heisenbergs-uncertainty-principle-is-proven-false/