It's all variable but if you have your degree, you could start looking for commissioning opportunities at your base after your enlistment / tech school.

For me, I enlisted straight out of HS to the guard, got my degree, then my MBA, then after 16 years enlisted I'm going to OTS tomorrow oddly enough. I applied for an officer job 2 years ago and finally I'll commission in 2 months.

But a 16 year gap isn't the norm, you could commission within 4 years if you wanted to.

I have no idea what your situation is, but just knowing that you have your degree, it's worth considering going guard/reserves and getting grad school paid for with the GI Bill and then applying for commissions.

I only say this because you've missed out on the ROTC boat and are worried about competitiveness being non-prior.

A recruiter would have a much better feel for your chances of going active, but this is a possibility for you.