This must be an exciting time for you and your family.
You may be able to purchase a home in VA using a loan product depending on your employment status and income to debt ratios and if you have any US credit trade lines open.
Have you been paying taxes through your ITIN?
I would recommend you contact a reputable lender. I know several fabulous ones!
Feel free to contact me and I will share their name and numbers/emails with you.