Can I submit an OCS packet if I am in AIT and have my bachelor's degree?

You cannot apply to OCS until you have completed AIT and arrived at your first duty station. Your branching is based on your OML through the program and the availability of branches at the time your class convenes (grades, physical fitness scores, etc.). Your past specialities may have some weight and you can bring that up through the accessions process or trade branches with one of your fellow candidates.

Now although the rules are written such that you can technically apply to OCS when you arrive at your first duty station, you need to understand that your packet requires full support of your chain of command. If you don’t have their support or the belief of the officers of your unit that you would be a good officer (and this is important to us), your packet will not move. Put yourself in their position. Soldier arrives from AIT in a billet they need. Brand new to the Army. First thing the Soldier does is request to begin an OCS accessions process. I’ve seen this before. It’s not pretty.

My recommendation: go to your unit. Perform well. Learn about the Army from the enlisted side. Pay attention to the things you learn like leadership, property, Army systems, and the values. Pick up Sergeant. Then decide if officership is the thing for you. If you are a tight performer, you will get a smooth process for your packet.

CPT Sharp absolutely nailed it. I don't think anyone could've said it better.

Technically until you have your MOS, you what not lived up to your contract, therefor I doubt they would pay attention to your packet.