From what I can see on the official UTA website, it is impossible to get farther than Salt Lake City on a Sunday night.
It is possible to take the 704 to the Arena station as the last train departs at 11:16PM on a Sunday night.
However the only public bus to Park City is the 902 line, which doesn’t run on the weekends.
Therefore you could either get a cheap hotel in Salt Lake City and wait until the morning or take a cab from the city center.
Credit:stackoverflow.com‘