Do you have permanent residency status yet? If not, you may need to wait. But adoption is all about waiting, anyway. Been there done that.
Also, you state you want to adopt an Asian American? Donmestic adoption is generally either private, which means arranged by agreement between birthparent(s) and adoptive parents through an attorney or agency. With these adoptions, be prepared to "staqrt over" once or twice, at least, as bioparents are inclined to change their minds after birth.
Domestic adoption can ALSO be through foster to adoption programs. The child would usually be older, not a newborn, and the bioparents could very well meet reunification requirments and the adoption would not take place.
I adopted internationally, from an orphanage, because I wanted to complete the adoption once and for all, and not risk losing my child. With the orphanage adoption, bioparents rights are often already terminated even BEFORE they country allows a referral to occur. My daughter was 2 when we got her.
Also, you wrote "I" want to adopt. You MUST adopt with your spouse.