Navy cutoff for non-prior enlisted pilot is 27, but I think NFOs can apply up to 35 or so. Get on Navy.com and find an officer recruiter. NFO would get you in the plane and in the air, but not flying it unfortunately. Depending on the platform you select you would be in the backseat of an F-18 or back in the tube of an E-2, among other options.
Route would be to finish your degree then go to OCS in Newport, RI. Then API training in Pensacola, FL, and onward from there. If you're interested in that you can PM me, I went the pilot route but we parallel trained with NFO's for a while and I still keep in touch with a few of them. Again it would get you in the air but you wouldn't be the one flying it.