In the military at 17 he's legally an adult since his parents had to surrender their parental rights for him to join.
Even if he's still considered a minor, a minor can NOT back out on a contract for essential goods and services such as food or shelter. This is a common misconception with relation to minors and contract law.
All of this said, the odds of qualifying for a loan are long due to your ages, limited incomes, and credit history. Not being married compounds the matter.
I would strongly urge the two of you to put the matter of buying a home on the back burner for now. He will need 2 years of service to qualify for an in-service VA loan and those 2 years will give you time to get both your relationship and finances on an even keel.
Just as important is getting married. Since he's not married to you, if he gets orders, you cannot accompany him at government expense. That will cool a budding relationship very quickly. If you are married, you can accompany him on most assignments even to foreign countries. (Obviously you cannot accompany him to a combat zone, but most GIs are not stationed in combat zones even with 2 on-going wars.) He will also receive significant extra money from housing and subsistence allowances if he is married. That extra money can make home ownership a reality; without it it's little more than a dream.
Retired First Sergeant