How do the fundamental quantum fields create particles? According to QFT, particles are excitation of their respective fields (electrons are the excited quanta of the electron field, photons for the electromagnetic field, etc). This excitement is due to the energy being placed in the field therefore raising the field out of the zero-point energy state. Though I am confused on how the particles/excitement became to be in the first place if all the fields are defaulted in the vacuum state? Do they self-excite themselves so they can then interact with the other fields? I guess that would be related to virtual particles, however I believe they are just mathematical artifacts. Did the big bang create the particles in the first place to allow the fields to interact and excite each other? Sorry if this was confusing, I am a layman.
 A: You are probably wrongly assuming that the universe before the Big Bang was in the vacuum state. But to my knowledge, there does not exist a widely accepted theory about what caused the Big Bang or what was before the Big Bang. The Big Bang is the name for the process that was initiated as a consequence of the otherwise unexplained initial conditions of the universe. To put it a little more colloquially: "Big Bang means we don't know what happened before or if anything happened before it at all". Hence, we also don't know where all the energy that the universe (which includes all its particles at any time) is composed of came from.
A: For a layman explanation, the fields are just a coordinate system for each particle. If no particle comes along to model its behavior, the electron field is inactive. When one wants to model a free electron with quantum field theory one uses differential creation and annihilation operators , operating on the mathematical wave functions that represent the field. To model an electron with a given energy and momentum, one can model  a track, by sequentially creating and annihilating with the operators on the wave function representing  the electron  field, a track.
There is a problem with this since the wavefunction representing the field is a plane wave, and the probability for the electron to be localized in one spot is infinitesimally small. One has to use the wavepacket solution , in order to localize a free electron.
But representing the track of a free electron  in QFT is no use, since the classical electrodynamics can do it mach better. Where the field and creation and annihilation operators are useful is in modeling particle interactions and decays, with Feynman diagrams, where creation and annihilation operators work at the vertices, giving rise to the formulae that are used to calculate scattering crossections and decays and more complicated stuff.
The fields themselves are inanimate, it is the creation and annihilation on the fields that creates/models  the particles.
A: Good question! It was the superfast expansion of the universe that pulled them into real being. Like two photons can create a particle/antiparticle pair, or a particle/antiparticle pair can excite two photons, gravitons can do the same. This happened during inflation and in a sense all these particles are still virtual. Quarks, leptons, photons, etc. All were excited from their virtuality into reality back then. From a  fluctuating existence in time, with unrelated energies and momenta, they got an existence with a direction in time while obeying the relativistic energy-momentum relation ($E^2 -p^2=m^2$, $c=1$).
