In QFT it's really the same physical story, just expressed differently. I'm not sure how much mathematical background you have, so I'll avoid equations, but if you want me to be more explicit, I'll edit the answer.
QFT is based on the concept of second quantization, which is what you refer to as exciting the quantum fields: just like a guitar string can be excited, so can the fundamental field of a particular particle species. Each such excitation is said to be a quantum of the field, and this quantum is what we call a particle. These fields can interact, and just like in regular QM or even classical mechanics, these interactions are expressed as terms in the Lagrangian/Hamiltonian of the theory. Basically, you can just think of this excitation, i.e. a particle, as propagating through space, “hitting” some other excitation of the same or a different field, and as a result exciting other quanta of various fields.
Now, if you want to calculate the probability amplitude of a set of particles being converted to some other set of particles through a collision, you'd compute the matrix element between the in state of the incoming particles (e.g. two protons) and the out state of the resulting particles, sandwiching the time evolution operator. If your fields can interact, i.e. some appropriate interaction terms appear in your theory, you may have a nonzero matrix element between them, which would mean that you will sometimes see the those particles coming out of the collision.
So like I said, physically it's the same story as what you have in mind with gluon fusion etc. QFT is really just the appropriate framework for doing such calculations, because it's manifestly relativistic (so you don't need to worry about causality) and utilizes the useful concept of second quantization, i.e. creation and annihilation of particles as excitation of the corresponding field.