I frequently try to assist new players on Newcomer Chat and a question came up recently that I didn’t know the answer to, and couldn’t immediately find an answer for.
So, if a brand new player buys WoW (whether from scratch or after having tried it out on the trial) and they have not yet reached 60 on any character, is the 60 boost character immediately available to them?
Or do they have to wait to reach 60 on another character before they can use it?
As long as it’s the Heroic or Epic edition of Dragonflight, they get the boost shortly after they upgrade to it. It’s not instant, but it also does not require that they already have a character at level 60 
The purpose of the boost was to allow players who just joined the game to play with their friends who already do. They didn’t have to play the game for days/weeks/months to get to current content. Just remember it’s supposed to be final. It can’t be undone except in specific circumstances. Deleting the boosted character doesn’t restore the boost. (I’ve seen players posting in Customer Support that seemed to believe it does.)
You do not need to have a level 60 character to use the character boost, it is immediately available.
Character Boosts were originally intended to allow new and returning players to jump into the game and play with their friends. While they would be skipping a lot of the leveling experience meant to teach new players how to play the game and their class/spec, the hope is that the friends they are joining will help them out in that regard. 
Thanks for being one of the many helpful folk who choose to spend their time helping new players. <3