[url]https://www.youtube.com/watch?v=vMPZHX7Mfn8[/url] is a recording recently posted of the Police playing the Nashville Room on March 6, 1977. The posting claims that it is the earliest Police bootleg recording, and I am unaware of an earlier one.
This was just the 4th ever public performance of the band, which was opening for Cherry Vanilla. Henry Padovani was the guitarist and the performance pre-dates Andy Summers joining the band by several months.
There is a write up of the show on Police Wiki at:
[url]http://www.thepolicewiki.org/Police_wiki/index.php?title=1977-03-06[/url] There may be some doubt as to whether the performance recording is this precise date but near that even if not then.
The set list on Police Wiki is correct, which includes a couple songs not listed on the youtube description. Here is the set list:
Landlord
Kids To Blame (Stewart song from Curved Air times)
Clowns Revenge (Sonja Kristina song)
Grand Hotel (Sting song from Last Exit times)
It's My Life (The Animals)
Dead End Job
Fall Out