Charge is a way we quantity how a particle is coupled to the EM filed. So what makes a particle charged is by interacting with the EM filed. And we can assign a value we call charge to a particle which is our way of describing this.
The EM filed is rather fundamental or at least a measurable thing that exists and certainly particles interact with it.
I can also refer you to [this](https://youtu.be/esayi49OAk4?feature=shared) video which you may find interesting.
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