How can a young man marry an American girl an 'urfi' marriage that is not forbidden, with the knowledge of his and her parents, and his ability to bear responsibility?

Legitimate marriage has conditions and pillars without which it is invalid, including the guardian and witnesses. If you wish to marry the girl, it must be with an offer from her guardian and acceptance from you, in the presence of two Muslim witnesses, and the marriage must be permanent. As for marriage with the intention of divorce after a specified or unspecified period, or marriage on the condition of divorce if she does not agree, it is an invalid marriage. However, if you do not stipulate that in the contract and merely intend it in your heart, the marriage is valid according to the majority of scholars. Documenting the marriage is not a condition for its validity, but it is necessary to preserve rights.