It really just depends on where you want to start the adventure. Given that the characters will likely be 4th-5th level at the end of LMoP, you don't have to use any side treks, instead just plopping the party directly into the main line of the adventure. Here are several options.
1) Instead of a map, perhaps a letter from one of the cults referring to ambushing the delegation. Have one of the delegates be a relative of Gundren, so Gundren asks the party to rush to the valley to help. [This starts them with the Missing Delegation quest.]
2) A map to the Necromancer's Cave side trek. [This gives them the opportunity to gain some goodwill in Red Larch, assuming they save the kid.]
3) A letter referring to the Tomb of Moving Stones under Red Larch, perhaps mentioning something about the Black Earth. [This gets them directly into the secrets in Red Larch.]
4) A letter referring to delivering trained hippogriffs to some Waterdhavian nobles in a place called Feathergale Spire, located in the Dessarin Valley. [This gets them to the first and easiest Temple outpost.]
