Health insurance carriers will offer coverage to those who are not U.S. citizens, but most of them require residency in the U.S. for a certain period of time. The most common requirement is 6 months of living in the U.S.
Carriers will often require proof such as rent or mortgage payments, utility payments or employment. A few carriers require one year of residency in the U.S and one carrier (Humana) requires two years. Suprisingly, there is only one carrier that does not require a minimum period of residency.