AFAIK the only way you can rush a report is to order a rush score, which costs extra.
NYU’s website says they will accept a test score if submitted by your school counselor…contact your GC, take a screen shot of your score, and ask if they will sign that and send to NYU. I’m not sure if CB allows you to download a pdf of your score, but if so, the GC could send that.
https://www.nyu.edu/admissions/undergraduate-admissions/how-to-apply/standardized-tests.html
Good luck.
Edited to add: Just confirmed that you can download your score report on the CB site. Choose a test, then you should see ‘download score report’ on the upper right. Download the score(s) you want, and ask your GC to email it to the address at the link above.