How can I possibly get assigned to 10th Group after Airborne school?

You can’t. You don’t get to choose your follow in assignment and HRC almost never gives you a follow on assignment of your current post unless you’re MACP or a very limited assignment MOS.
But after your next assignment you can possibly reenlist for 10th SFG.

It depends on what you want to do, and why you want to go to 10SFG. 10SFG is an Airborne unit, so you could go over there and then have them send you to ABN School. It would be expected that you go to ABN if assigned to that unit. Going the other way (re-enlisting for the purpose of going to ABN) might get you to school, but after that they Army will put you where they need you most.

If your intent is to get tabbed, then you need to drop a packet for SFAS. But SOF units require enablers, so if that's what you're interested in I'd talk to both HRC and someone in personnel at 10SFG(A). It certainly helps, as others have indicated, to have someone that will vouch for you and to be requested by name for a certain position. On the other hand, a lot of the junior enablers in the various staff sections come right out of AIT. Not everyone agrees with that, but that's how it it works at the moment. You also have Group Support Battalions (GSBs) that are going to have a lot of the enablers that support SOF missions (i.e. UAV operators, chemical decon, etc.) where you might also look at going.

You have to take/pass SFQAS and be selected, a tough row to hoe, and absolutely no guarantees

HRC does control your future at this point, but it can not stop you from going across post and speaking with the group CSM and talking about available billets and intrapost transfer (by name request). Soldiers with moxie, purpose and motivation are hard to come by and will generally not be passed on in my experience. Good luck.

Speak with your branch manager. Or contact GRPS1 talk to their strength/CMF manager and see if they have a spot available if so you can try a interpost transfer.

Might get lucky if you know someone at the STB portion of the Group, but unless you have a full bird in your back pocket you might not be able to be so in command of your position.

You might have to talk with your folks in personnel about that. Assignment to a particular unit often entails a letter acceptance by someone of authority in the unit. Also, you are going to have to consider factors such as your MOS/CMF and the needs of the Army. While you might be able to get a slot as a rigger, mechanic, radio repairman, etc., you would have to meet all the pre-requisites to even volunteer for duty with an SFODA. Hope this helps. Good luck.

Thank you all for the responses, I’ve spoke with a buddy of mine who is currently assigned to 10th Group and he advised my best bet is to call the SGM directly to inquire about possibly being assigned there.