I recently asked the question (with title "electron charge") about the negative charge of an electron and I received several answers to tell me that what I had heard about the formation of the electron was in fact erroneous. I had in fact figured this out but the question still remains, namely " how is an electron made?"
Electrons are formed in the following processes:
- The decay of a more massive lepton e.g. the decay of a muon.
- The decay of a $W^-$ boson, usually as part of a weak decay process e.g. beta decay.
- Pair production, where a high energy photon produces an electron/positron pair.
(There may be other processes as well ...).
The standard model of particle physics takes as axiomatic the table of elementary particles
Axiomatic means "given" so the existence of electrons is a basic assumption of the current theory, which is of course based on observations of single electrons.
It depends on the framework of the question then on how a given electron is "made", i.e. appears and is measurable. In the Big Bang theory, during the electroweak epoch, electrons appear with the mass given in the table after symmetry breaking. To understand this will need years of study starting with quantum mechanics then field theory then cosmology.
In every day laboratory frameworks electrons appear in a number of interactions as described in the answer by gandalf61.