Hi there. As TakeruK said, a good supervisor won't say yes from the beginning, and you may want to send another email, with more details or with another approach. I had a friend in this situation, but he ended up applying without a supervisor, but his case was a little different, and as much as I know, everything went ok. You can also find a piece of advice on https://www.vocationaltraininghq.com/how-to-become/construction-manager/ concerning your future career, but not only. Good luck and don't be discouraged.