We do have examples of billions upon billions of tonnes of iron being moved that have altered (slightly) the spin axis, also examples of ground water pumping at scales that have done the same .. but I'm unaware of any mountain sized objects that have vanished overnight.
“Nothing happens unless it has an explanation within the laws of physics” is an assumption; if it was broken then it would be broken. The mountain would be inexplicably gone, not explicably gone.
In that hypothetical, there could be testable proof of "a magic event occurred" without magic becoming part of science.
That said, in the cut and thrust of conversation and or debate the example by dialogue isn't perhaps as clear cut a device as it may have seemed from your keyboard.
That might just be my reading <shrug>
Yes, I get your point...
Man: "Uhh..."
God: "How can you rectify quantum mechanics and relativity into a single coherent model? How does physics work, exactly?"
Man: "Well, you see, um. Hmm."
God: "And the Collatz Conjecture? Why does it always trend to 1?"
Man: "I'm obliged to say magic because I don't have a better answer?"
God: "Exactly. I did magic for all of those ones"