The field is the more fundamental entity

I will quote Barak Shoshany answer to the question “What is the relationship between a particle and a field?” on Quora:

A field is a mathematical entity that exists throughout space and time. A classical field is simply a function that has a numerical value at each point in spacetime. Think, for example, of the temperature in a room: in principle you can define a function T(x,t) that gives the temperature at any point x in the room at any time t. Fields are defined similarly.

A quantum field is what you get when you “quantize” a classical field. In this process, the field becomes a function that gives an operator at each point in spacetime, instead of a numerical value. I won’t get into detail about the mathematics of quantization or what it means to have a operator-valued function.

A particle is an excited state of a field. What this means is (roughly) that a particular system may be in a vacuum state (0 particles) or in various excited states of the field (1 or more particles). The field operators may be used to create or destroy excited states (and thus, particles) at particular points in spacetime.

We call the particle associated with a field the “quantum” (plural “quanta”) of that field. So, the photon is the quantum of the electromagnetic field, the electron and the positron are the quanta of the electron field, and so on.

Therefore, the field is the more “fundamental” entity; the field exists everywhere, and the particles associated with it are arbitrarily created or destroyed by the field operators whenever they are needed, or even just at random (by “quantum fluctuations”).