The Muggle World
Voldemort had spies throughout the Ministry.
Dumbledore had at least one spy in the Death Eaters, and probably more in the Ministry.
Why wouldn't the Muggle government have its own competent spies in the magic world?
Once Voldemort fell, they would have at least been to a few of the public trials, where the Azkaban Death Eaters would claim that Voldemort would be back.
Also, they would read the Prophet and see that, not only did Harry Potter survive the killing curse, but would also have the names of his parents. That would be investigated, and the Dursleys would pop up on their radar.
A quick covert investigation of the Dursleys would have Harry grabbed by the Muggle government and raised with a family in the know. He would be checked out in a medical way, where the horcrux would be found and (hopefully) removed.
It also would lead to at least research into what it was and how to find the rest.
Harry himself would grow up in a loving muggle (or more likely muggle-born) home (probably under a pseudonym). He would be trained in magic (early magic studies either in the UK or abroad) and survival skills (in a group like the Boy Scouts). He'd be (at least) somewhat prepared to reenter the magical world.
All this while Dumbledore is freaking out from losing The-Boy-Who-Lived...