Is it permissible for me to marry a young man who is two years younger than me, given that he fears his family's rejection of this marriage because I am older than him, even though his family knows me and approves of me?

There is nothing in Islamic law that prevents a man from marrying a woman older than him, or vice versa, if both parties consent. The Prophet, peace and blessings be upon him, married Khadijah, may Allah be pleased with her, and she was older than him. He also married Aisha, may Allah be pleased with her, and she was younger than him. Umar ibn al-Khattab, may Allah be pleased with him, married the daughter of Ali ibn Abi Talib, may Allah be pleased with him, and she was much younger than him.

One must be careful about women mixing with non-mahram (definition) men and speaking with them. Therefore, you must stop speaking with the man and avoid being alone with him. If he wishes to marry, he should approach your guardian. Also, the marriage must be with the guardian's consent.