Did electric charge not exist in the early universe? I ask this question based on something Don Lincoln said in a video about leptogenesis over at the Fermilab Youtube channel. Video for reference: https://www.youtube.com/watch?v=PsqEcGMjEfo
Here is his exact quote:

... during a time in the universe very shortly after the Big Bang -
far less than a trillionth of a second after the cosmos began ... the
universe was extremely hot - much, much, hotter than we can achieve in
any conceivable particle accelerator.
...there is a ghostly field in the universe called the Higgs field
that gives mass to subatomic particles. The Higgs field depends on the
temperature, which is to say, the energy, of the universe. Above that
temperature, the Higgs field is zero, meaning that all of the familiar
particles have no mass.
...This is kind of hard to imagine, as the universe was way different
than we currently understand, with properties like mass and even
electrical charge not existing yet.

What is he referring to? Did electric charge not exist in the early universe? And does that have something to do with the Higgs field being zero?
 A: In the earliest part of the big bang, the electromagnetic force had not yet split out from the unification of all the forces because it was still too hot for this to happen. At that point in the process, there were fractionally-charged quarks in existence but they didn't "talk" to one another electromagnetically. Things had to cool off some more before electromagnetism could split off and electrons and positrons could exist, and start to interact electromagnetically. See Stephen Weinberg's book The First Three Minutes for an excellent and detailed account of all this.
I do not know if this history depends at all on the Higgs field.
A: In a sense electric charge did exist before electroweak symmetry breaking, in another sense it didn't.
The following analogy is a bit silly but it's the first thing that popped into my head.
You have a box, inside of which is a pencil, and you're shaking the box so that the pencil bounces around inside it, pointing every which way. Eventually you stop shaking the box and set it down, and the pencil stops moving. It now points in a particular direction.
Did that direction exist when you were still shaking the container? In one sense yes: you could have pointed in that direction at any time. In another sense no: it would have made no sense to point in that direction before you knew that the pencil would end up pointing that way.
This is not too different from what happens in electroweak symmetry breaking. Electromagnetism is associated with a "direction", not in the usual three spatial dimensions but in additional dimensions whose true nature is still unclear (and out of scope for this question in any case). When the temperature drops, the fields settle down into a state where one direction is singled out.
The pencil represents the Higgs field, more or less. The Higgs field is not zero but chaotic at high temperature. The particles don't have zero electric charge (or mass), but no electric charge (or mass)—i.e., it doesn't really make sense to assign a number, even zero. It's common to describe the particles as massless before EWSB, but it's misleading, since "massless" usually means a mass of zero.
