My dad was deported and re-entered the US illegally, is there a possibility he can get his green card if I join the military?

I’m not joining the military solely because I want my parents to get their green card, although is a huge benefit that comes with it, it’s not the only reason I’m enlisting.

Now that being said, back in 2005 my dad was deported and came back in 2006 to raise me (my mother had just given birth to me at the time) My dad has been a law abiding citizen ever since. He’s never gotten in trouble with the law, never got government assistance and worked hard for our family and pays his taxes. I’m hoping to get an answer regarding his future when I enlist for active duty soon, I’m close to signing my contract and after I do I plan to bring it to an immigration lawyer, but recently my dad has gotten worried on the outcome. He’s worried about there being no possibility to help him out. Can me enlisting for the US army help my father’s case despite his previous deportation?

Edit: I’ve seen a lot of people nitpicking how I’ve written about my situation. I’m thankful for the honesty about my case from the individuals actually trying to help. I hope this post can help someone going through my case with an answer!!

EDIT 2!! Fuck all the assholes giving me shit, I asked a simple question. I wanted an answer, not people making fun of the situation thru dms and comments. no my dad isn’t a criminal in my eyes, but he may be to the law. I’m understanding of this, no reason so be a dick about it..