Is it permissible for a 20-year-old young man studying at the Faculty of Dentistry to seek marriage despite not having money, or must he wait until he graduates, gets appointed, and has sufficient money for marriage?

There is no harm in seeking marriage even without money, for marriage is one of the best acts of worship, and it contains many benefits. Allah and His Messenger have commanded it, and Allah has promised to enrich the poor person who marries. Studying does not prevent marriage, and early marriage has many advantages. If marriage is not possible, then you must work on chastity and steadfastness in obedience to Allah.