An electron is an excitation of the electron field. So when we observe a higgs boson that means we've excited the higgs field?

See this related question: If particles are excitations what are their fields?

I ask this question because, according to a lecture, the higgs boson was frozen into a "matrix" at some point before recombination (otherwise we would not have atoms). Is this considered a field in the same way an electron field is a field? It was described that higgs was everywhere ... Is that another way of saying there is Higgs field?

This means the electron interacts with the higgs field and not with excitations of the higgs field? Or probably Higgs bosons are only excited momentarily.

Was the electron field also created like the higgs field at some point?

See here https://www.youtube.com/watch?v=hL2BLAOVbDA