"Is it simply a matter of luck that out of all the hats in the game, they just happened to craft one of the new ones?"
"Are there any craft recipes I can use to increase my chances of getting a low craft number item?"
If the item happens to launch with a specific recipe, then of course you can use that recipe to craft it. This is generally pretty rare, however. More likely is that you can use the Fabricate Class Weapon (1 scrap, 1 class token, and 1 slot token) or Fabricate Class Headgear (4 refined metal and 1 class token) to fabricate a weapon or hat that belongs to a specific class. If all you care about is getting a low craft number, then use the class token for the class with the most weapons or hats for that update. (See the wiki for more.)
"How can I anticipate when an update is released with new items so I can be ready to launch the game to begin crafting?"
Big updates are advertised on the Official Team Fortress 2 Blog. I recommend you subscribe to their RSS feed. Alternatively, you can read the Steam Powered User Forums to stay informed.
"Is attempting to obtain low craft number items a roulette similar to crate unboxing, or is there any strategy behind it?"
Watch Steam all day (particularly in the early evening pacific time) when the update is supposed to drop, then craft like mad. You'll want to stockpile refined metal and/or craftable hats. Aside from the few tips I've given to improve your chances, the item you receive is completely random.