you basically can go through the Navy side of the program all the way up to partially through your junior year before the transfer to the Marine options must occur. You will most likely put in your package toward the beginning of the school year.
I had two friends who did this my junior year of college, transferred, completed OCS, and are now at TBS.
If you want to do a little of the leg work for yourself, google Regulations for Officer Development (the ROD). Its a large .pdf document that will tell you everything you need to know and more about your NROTC unit.