Why is quantum mechanics ab initio ?
A plethora of phenomena and higher order ‘laws’ could be deduced from it by putting in the appropriate hamiltonian e.g tunneling,spectra of atoms/molecules,bandgaps in semiconductors,blackbody radiation.. Take a quantum system, (a system for which a classical description will give the wrong predictions) subject to certain constraints translate those to boundary/initial conditions and falsify experimentally whether the system behaves as predicted.
Classical mechanics ?
Our every day world (buildings standing, objects falling, geological phenomena,..) seem rather well described with newtonian mechanics formulated in a suitable formalism.
Classical electromagnetism ?
In the regime where it applies you could use maxwell’s equations ?