I thought about replacing the ‘Romeo and Juliet’ play with a self-written play. “When he meets an exchange student, a socially awkward nerd joins the university play to win the lead role and have his first kiss ever with his crush before she returns to her home country.”

" I know many actors who are socially awkward, yet on stage they shine.How about you make him an introvert."

Someone being an introvert doesn't necessarily mean they have stage fright. I suggest using stage fright or anxiety. ?Stage fright is a trait which directly hinders his ability to complete his goal, but I agree social awkwardness isn't the best description.?

The inciting incident is mundane, best you describe it as a significant event instead.

After falling in love at first sight, a...

The MC description doesn't give him an obstacel that directly relates to the obstacle he will face - I know many actors who are socially awkward, yet on stage they shine.

How about you make him an introvert.

Here is my try:
After falling in love at first sight with an exchange drama student, an introvert auditions for the part of Romeo so he can kiss his Juliet in the school play before she moves back to her home country.

I would say "paralyzing stage fright" or something of the sort so the audience understand the stakes and what the lead must overcome.