The first official UFO sighting didn't happen until after the first and other nuclear bombs were set off. That part is an actual fact. It happened in 1947.
It's isn't and it didn't. That fact is no fact at all.
Formal reporting of UFOs in
US archives can be traced back to at least as early as October 1944, with 'foo fighter' sightings by the 422 Night Fighter Squadron operating over Belgium and Germany. That's followed by more reports from the 415th NFS during November 1944. That's more than six months before the Trinity tests.
Elsewhere, "official" sightings can be traced back even earlier.
UK reporting of UFOs to Bomber Command starts in May 1942 (with reports of 'aluminium cigars' flying at upwards of 500mph). By November 1942, the Bomber Command Operational Research Section was publishing reports on individual sightings. In individual RAF unit diaries, reports of unidentified flying objects can be traced back to mid to late 1940.
German reporting of UFOs can be traced back to a similar timeframe - German pilots report 'bright lights', 'balls of fire', 'glowing orbs' and similar as early as 1940. Similarly, there were Japanese reports of UFOs in the Dutch East Indies (now Indonesia) in 1941-1942.
If you want to stretch the definition of "official", you can also look up newspaper reports of 'phantom airships' from the 1890s in the US, and from 1912/1913 in the UK. I believe there may have been an official investigation into the UK one, as the Admiralty was very worried about Germans using airships for reconnaissance and bombing.
Some reading on WW2 reports of unidentified aerial phenomenon (this is by no means an exhaustive source)