What's fundamental is the Coulomb force. If we place two charged particles near each other, they experience an attractive or repulsive force, depending on whether they are opposite or like charges. We can measure that force directly, for example if the charges are on the plates of an electroscope, by observing the deflection of the plates.
The electric field is an abstraction of that force, allowing us to predict what force a hypothetical charge might experience if placed near some other charge. A mathematical construct that we can imagine into existence at any time.
The electric potential is then a further abstraction, the integral of the field along a path between two points.
In electrodynamics (as opposed to electrostatics which I've been talking about up to now), we can produce a non-conservative electric field. This happens typically when the field is produced by a changing magnetic field rather than by a charged particle. In this case we can still in principle measure the force produced on a charged particle (You could calculate the forces that are required on each electron in an antenna to account for their motion when they are receiving a radio signal, for example). But the scalar potential isn't even a defined quantity since the integral of the electric field will be different for different paths between your two points.