If you were Tywin Lannister during “The War of the Five Kings”, how would you conquer the North in the fastest and most efficient way?

We already know how to conquer the North in the “fastest and most efficient way” possible.

Do exactly what Canon!Tywin did in the books.

Chevauchee. Alliances with strategic partners. The odd round of sabotage. Tywin got a LOT of help from the entire Greyjoy BS (which is partly why I'll never give ASOIF a 10/10) but in general, the Lannister Strategy was pretty solid.

Essentially get Robb Stark to mess up his social contracts and then arrange for a suitable Northern replacement to step in and sign a peace.

The problems with this are two-fold.

1- It assumes that Robb Stark, born to rule the North, knows as much- or rather, as little-known about Medieval Social systems as the typical Modern Liberal Civilized Atheist.

2- It assumes that Tywin is not only as clueless as the aforementioned Robb Stark but that he's an omniscient tyrant with such absolute authority that he's beyond all social contracts and is basically a god to his vassals.

Word of advice- Don't read ASOIF for the Medieval politics. The story is great, the characterization is, a tad crazy, but brilliant, the themes are, though not original, dealt with well- but as a representation of a “Medieval World”, Westeros leaves much to be desired.