Ah okay; so all you have is your final rendered video; which is 4×3 letterboxed?
In that case; if you really want it to play fullscreen on YouTube, I’d create like a 1280×720 or 960×540 square pixel sequence in FCP; drag your letterboxed final file into that sequence, do NOT match sequence settings to clip settings; then manually scale up your video so that it fills the window and eliminates the black bars
Not ideal, and you’ll lose some quality of course.