Change of Visa status from B2 to F1

Hi! I am an Indian passport holder on B2 visa in the US due to a family exigency. I received admission in a doctoral program last week, I had applied for it in December 2020. I want to change my visa status from B2 to F1 as my classes start in Fall. I was planning on going to Mexico or Canada as India is not possible due to Covid surge. But even Mexico and Canada consulates are only taking emergency cases and the wait time is not visible online. Please guide.

You can file B2 to F1 change of status application with USCIS.

I do not want to file with USCIS as it takes top long and my classes start in August. Is Mmexico a good option for change in visa status?