What to do for my graduate school application if I think my GPA doesn't reflect my coursework mastery
An application for grad study in the US contains many elements, of which GPA is only one. If the GPA is poor, then the other elements need to indicate a high likelihood of success in graduate study and thereafter. Research experience (published papers especially) is a good indicator. And in the US, the letters of recommendation from people who know you well and can be expected to give an honest assessment can be very important.
Talk to some of your current professors and get their advice about how to proceed and ask for letters as appropriate.
And, you need the knowledge from those early courses, even if your GPA doesn't reflect that you have mastered it.

To respond to your edit:
No, the SoP is not the place for this and it will sound like an excuse there. That isn't to say that you couldn't mention it elsewhere, though it is best if the explanation is given by others, such as letter writers.
But, the SoP should be entirely forward looking, saying what you want to do in the future and not giving explanations about the past. Say, in the SoP what your plans are for graduate study and thereafter, including any ideas you might have about research areas you hope to explore. You likely have a limited amount of space/words in the SoP. Use them effectively.