Can I apply to college (full-time) before I ETS?

Check if COVID-19 affects school application or ETS since some schools may delay in-person classes depending on local conditions...

As early as the University accepts applications.

I applied before I ETSed. The school doesn't care, nor should the Army (as long as you apply on personal time of course). You should tell the school of your planned start date and meet the deadlines for that date.