Since quantum uncertainty (in a finite universe) basically says that you can't measure anything with infinite precision - I'd argue that God created, at most, the Rational Numbers. The Reals might be the closure ( https://en.wikipedia.org/wiki/Closure_(topology) ) of the Rationals - but doing that was the work of man.

Quantum mechanics actually contains measurable real numbers (well.. complex numbers). Amplitudes are postulated to be infinitely precise, and rounding them has a tendency to introduce pretty serious consequences like FTL communication.

For example, in fault tolerant quantum computing, rotations are synthesized using sequences of 45 degree rotations around the X, Y, and Z axes. The matrices that describe those 45 degree rotations contain rational and irrational numbers (in particular: sqrt(2)). If those irrational numbers are actually truncated, this would have observable consequences. You'd need a sufficiently large quantum computer running for sufficiently long to do sufficiently accurate tomography of sequences of those rotations in order to resolve the truncation, and to be frank some of those "sufficientlies" would be very impractical to achieve especially if the truncation was small (and woe unto you if adding more qubits somehow reduces the amount of truncation!), but in principle it'd be possible.