Is it permissible for us to supplicate to Allah to unite us in a lawful marriage, even though the young man is an expatriate and does not possess legal documents?

There is no harm in supplicating that Allah unite you both in goodness and in a blessed marriage, for supplication is among the best means a Muslim resorts to, and Allah has commanded it and promised to answer it. Istikhara should also be performed, for it is one of the greatest means of achieving success. If marriage becomes easy, then praise be to Allah; otherwise, let each of you go your separate ways, while being wary of the devil's inroads through emotional relationships.