AFAIK, for acquisition on the US federal government level:
1. It is not a problem if company owner is not a citizen and only has green card.
2. Government solicitations have FAR (Federal Aquisition Regulation) clauses attached to them. FAR 252.225 (Buy American Act) applies to many of them, but not all.
3. Some federal solicitations are set-asides (reserved for certain disadvantageous companies). From a source that's several years old but is still representative:
Federal set-aside goals:
23% for small businesses.
5% for SDB (small disadvantageous businesses).
5% for Woman Owned SB.
3% for HUBZone SB.
3% for service-disabled Veteran SB.
You are talking about qualifying for SDB. You should ask SBA if you qualify but I guess no.