Is it a bad thing to send an application for a master thesis late at night? I am looking at an advertised Masters thesis/internship that could lead to a PhD. The first contact should be made by email.

Is there any chance it could be looked down upon if I send that first email late at night?

I live (and currently study) in the same timezone as that of the research group, and that will be made evident by the contents of my first email.
Officially and practically, no. Applicants often worry about things that faculty hardly have time to even think through. Your application is understandably your central focus but it can't be the faculty's with the same level of attention.

In a nutshell, on the faculty side, I really can't imagine a colleague would care about that unless there were instructions for the time etc.