As far as I can tell, I am admittedly not a physicist, this is at least a contentious issue and probably, again as far as I can tell, a popular misconception. Those fields in quantum field theory are mathematical tools, one starts with particles and then defines fields to mathematically handle system where particles are created and annihilated.
Think about it, think about all physics you have ever done, in school or wherever. You have probably never dealt with a situation where something was created or destroyed. You need variables to describe all the things you are dealing with, how do you add new variables or get rid of some old variables halfway in your calculation when something is created or destroyed?
This is what those fields in Fock space are for, they are mathematical tools to keep track of the number of particles you have in specific states. You do not start with a field and discover that it has quanta behaving like particles, you start with particles and just describe them with fields in order to be able to handle particle creation and annihilation.
Here is Nima Arkani-Hamed giving the Salam lectures 2012, a five day series on the state of fundamental physics. I marked [1] about 30 seconds where he is very clear about this. You can also start here [2] and watch about 10 minutes of this lecture where he quickly redevelops the ideas of quantum field theory.
Even if you can not follow all the details, you should easily be able to follow the explanation where the fields come from and why. The particles vs fields issue is explicitly discussed three or four times within those 10 minutes. You may of course want to watch the entire lecture series, it is really good and is pretty non-technical in the beginning. The last day I linked to is actually the exception if I remember correctly, the first four days are mostly without math.
[1] https://www.youtube.com/watch?v=tnA7bh7dTqY&t=1669
[2] https://www.youtube.com/watch?v=tnA7bh7dTqY&t=370