Your professor has made a generous offer, I think. Your situation is difficult, I also think. It would be good if you could find a way to go, both for now and for your future prospects, both with the (prime age) professor and in meeting people.

So, the issue becomes funding. The first thing you might do is look for funding locally. It is entirely possible that your university has some funds that can be used to support students in such things. The place to start is with the department head, I would guess. See if there is some travel monies available as they certainly have for faculty. If not in the department, then possibly at a higher level in the university.

You may also belong to a professional organization as a student member. Many of these have travel grants available. You might look there.

Your professor has made a generous offer if these were personal funds, I think. Your situation is difficult, I also think. It would be good if you could find a way to go, both for now and for your future prospects, both with the (prime age) professor and in meeting people.

So, the issue becomes funding. The first thing you might do is look for funding locally. It is entirely possible that your university has some funds that can be used to support students in such things. The place to start is with the department head, I would guess. See if there is some travel monies available as they certainly have for faculty. If not in the department, then possibly at a higher level in the university.

You may also belong to a professional organization as a student member. Many of these have travel grants available. You might look there.

Another possible option is funding from the conference itself. Some conferences have some funds for student attendees. In some cases the students serve as "volunteers" during the conference, running errands, but can also attend as usual. The conference web site may have something about this, and the organizers may be able to offer suggestions if contacted.