SWE intern vs current startup role

Hi,

I am from EU and currently pursing Msc in CS. I have about 2.5 YOE and I would classify myself as a strong mid, but until now I didn’t have any opportunity to work at a big tech (or any known company really). Now I can join google as an intern, but now am I doubting whether it is worth it.

For the time of the internship, I would have to move to the other city within my country and accept salary cut in half. Is google on the cv worth it?

Should I try getting another offer in the same city that I live in? (Google has two hubs in my country)

Thanks