Does the first black site mission provided reset the Advent Project countdown timer?
Solution 1:
Yes, the Advent Blacksite mission reduces the Avatar-progress by 2 pips (Legend difficulty) and will stop the timer, if it's already running.
Other facilities will reduce the progress by the number of pips shown below the facility on the Geoscape.
Solution 2:
In the legendary game I just played, the clock did not reset.
I had 6 days left on the clock before doing the 1st game provided blacksite. A few minutes later Avatar got the 2 blocks back due to a dark event. And the clock was at 6 days - basically ending my game for me.