How can I get a conditional release signed by the TAG of my state without having to hand it to my unit?

You won't be able to process it without going through your unit. These things have steps. And step 1 is having your commander sign their approval/denial. If they are bad with papers as you say, then literally hand carry everything to everyone that needs to sign. Again, you will NOT be able to bypass your CoC.

First off congratulations on being a father. Getting married just because she is pregnant is a bad idea. So make sure that she is the one before you decide to marry her. I've seen far too many young Soldier's get married because they think they have to and it ends badly. As far as benefits are concerned if you aren't married it does create problems because the military won't recognize the child until its born. Then you would be eligible for dependent benefits. But anyways as far as the conditional release you have to go through the chain of command for their recommendations. And its not a quick process. It has to go up to the General level for approval. If you try and bypass any level it could also end up badly for you. Just remember the Army isn't a holy crap I need a job so I'll join career. If you want to serve on Active Duty then great I applaud but don't do it just because you think you are stuck and have to get married and will have a child to support.

I just want to say thank you all for your words of wisdom, and inspiration. I have turned in my packet for Active Duty to my CoC. I call every Friday to get updates on it, I personally don't care if they think I am annoying, lol. But thankfully I also found an ADOS position in a different state, and I took it. Since I will still be attached to my home unit, just working for another one, they will let me know when my packet is ready to be submitted to an active duty recruiter with all the right signatures!