If my professor does submit it by August, do you think that would be too late with all this COVID stuff going on?
People have had success applying in August (myself included lol), but with everything else going on, schools might be more lenient... BUT it's honestly really hard to say - other applicants may have everything together already, even with COVID happening, and that's who you're competing with for interviews and acceptances.
I would really, really try and ask your professor if they can submit it earlier since that's all your application and schools will be waiting on.