If you are there at early entry, you are funneled one way; you don’t have to make any decisions.
For IOA and Hagrid’s, the fastest way is to head towards Seuss Land. There is a split in the path when you enter the land, keep left for a ‘bypass’ that doesn’t take you through the heart of Seuss Land. At EE, they force you to go this way since the Seuss attractions aren’t open anyway.
From there, it’s a single path to Hagrids
Over at USO, go straight between minions and shrek. Past that, there are a few paths you could take and I’m not sure anyone is faster than the other. Basically, you’ll have to turn right down one of those paths, then a left when you get to the lagoon keeping the lagoon on your right.
I think the most common path(might be the fastest, but I don’t think there’s a big difference either way) is to make the right when you pass Monsters Cafe (which will be on your right).