Yes, classical electromagnetism is also an ab initio model. The central equations of these three theories are all derived from fundamental laws of physics.
1. In classical mechanics, we derive equations of motion starting knowing the law of universal gravitation F=GMm/r^2
2. In classical electromagnetism, we derive the Maxwell’s equations knowing Coulomb’s Law F=kQq/r^2
3. In quantum mechanics, we postulate/derive the Schroedinger equation
Now, quantum mechanics is the most tricky. The laws we start from in the classical theories can be easily and intuitively tested. Normally, the Schroedinger equation is postulated as a law of physics. Its actual derivation, or rather one of possible derivations, starts with the classical wave equation from electrodynamics. Then we use the relation E^2=p^2c^2+m^2c^4 to get the Klein-Gordon equation whose non-relativistic limit is the Shroedinger equation.
Everything in here is as fundamental as the classical laws, but we cannot really test in our homes the laws we treat as our “first principles”.