I know, Deanna Troi has called it Federation Day, and that may be an official name...
But Deanna was once a cake.
So that point is invalid...
On this day (in the fictional post nuclear war future), Zefram Cochrane launches the test ship, Phoenix, from Bozeman, Montana.
It was the first Earth ship capable of warp speed.
The test flight caught the attention of alien life that was passing the solar system, interested to see that humans had developed interstellar travel.
So they landed.
And as Star Trek lore remembers, were the Vulcans.
And Earth had it's first (official) contact with alien life.
And everything changed.
And The Adventure Continued, and Continues.
...Granted that leads to Insurrection. We don't talk about Insurrection.
HAPPY FIRST CONTACT DAY!