Is there any adventure paths that start above level 1?

[Kyubey_]

Something perhaps level 3 or 4?

[PossibleCabbage]

A lot of APs you could plausibly just skip the first book and just inform the PCs about the relevant information which would have been gleaned in the adventure. Carrion Crown is a notable example.

[Skeld]

Kyubey_ wrote:

Something perhaps level 3 or 4?

Officially? No. They all start at level 1, as published.

-Skeld

[CorvusMask]

Unless they try out "3 part AP" thing in Pathfinder 2e as well, yeah all of them are going to start from first level. I think 3 part aps would be the only exception because they are used with assumption you can either run them back to back or as part of another campaign.

[PFRPGrognard]

They start at whatever level you like. Every installment is written to work as part of the larger adventure path or run independently.

[Shaun Hocking]

There's no reason that you couldn't start any AP with 3rd level characters. Sure the PCs might find it easy but you could bump up a couple of encounters or just let them enjoy being a bit extra useful early on. 5000xp (for being 3rd level) quickly becomes a meaningless amount as the AP progresses and you'll soon find they are at the right level for the AP by the end of book one anyway.