Changing from F2 to F1 visa


I have applied for a University. I am currently on F2 visa. I can apply for COS only when I get I-20. I have applied for Fall Semester. It will take 2-3 months as it is mostly mentioned for USCIS to process my F1 visa. This might extend beyond October semester. I do not wish to travel to India. Is it ok if I ask University to postpone my admission for the next Semester at this point or wait till my I-20 gets processed?

Also can please someone guide me for the procedure to apply for COS.

Please advise