I'm reading in Tales of the Quantum (page 68) that "Each neutron is made up of one up quark and two down quarks. In a free neutron one of the down quarks will transform into an up quark, turning the neutron into a proton and creating an electron in the process."
Where does that electron come from?
Here's an analogy that might help.
When an electron jumps from a higher orbital to a lower one, it produces a photon which carries away both energy and angular momentum. This is the energy difference and angular momentum difference between these two electron orbits.
When a neutron turns into a proton, the quarks change from an udd to an uud. So a down quark is changing into an up quark. This change is similar to when the electron changed orbits, but with a couple of key differences.
In the case of a down quark turning into an up quark instead of a photon, a $W^-$ virtual particle is created. It's virtual because the W's have mass and there isn't enough energy in this transition to account for this mass. But quantum mechanics will let this happen in its funny way.
The $W^-$ carries aways some energy, angular momentum and some electric charge. The $W^-$ isn't stable, and so will decay into an electron and an antineutrino. The electron and neutrino have a lower mass than the difference between the d and the u quark, and so the energy of transition is able to create real versions of them.
Over the full story, the energy, angular momentum and charge are all accounted for.
There are some nuances that I've glossed over, but that is pretty close to the legit picture.
This was actually why physicists (Wolfgang Pauli, Enrico Fermi) started to think that neutrinos and antineutrinos were a thing.
On its own, the electron that is produced doesn't have enough energy to account for the change in mass from the neutron to the proton. It also doesn't the right amount of angular momentum. So there must have been some other (hard to detect) particle that was carrying away the extra energy and angular momentum.
You might check out the story of the neutrino.
It is very important to understand, and accept that the universe is set up so, that if certain laws are obeyed, certain particles and energy can be transformed into other formes of particles and energy.
There are many examples of this, like pair creation, with photons and electron positron pairs, but your case is one of these transformations too.
What needs to be obeyed is energy and momentum conservation (and other laws), but if these are obeyed, then the part of the total energy in the process might as you can see be converted into an electron.
Another example for your question is asking where the neutrino comes from in weak decay processes.
Or you could ask where does the photon come from when an electron/atom emits it.
So you are asking where the electron comes from, and the answer is that it has always been there (in a different form of energy), and it comes from the total energy in the process that is available.
