In my experience this question is usually built on the assumption that Troy ceased to exist at the end of the Bronze Age. It didn't. Other than a break lasting roughly 950 to 750 BCE, it was continually inhabited until close to the 1300s CE. So, in answer to your question:
Schliemann didn't find the site; the site had never been lost. What Schliemann did was to disprove an ancient theory that the city had moved around over the centuries. And even in that he was beaten to the punch by Charles McLaren in 1822. Schliemann himself purposely distorted and obfuscated genuine historical arguments in order to cast himself as discovering something no one had believed existed.
The evidence includes tons and tons and tons of archaeology; coins specifying the city; a few dozen inscriptions (you can narrow them down geographically by clicking on 'All regions' at the bottom and selecting 'Asia Minor', then 'Troas'); loads of contemporary references to it (including Strabo's detailed account of the topography of the Troad); many attestations of historical events in the city including visits by people like Xerxes, Alexander, and Cornelius Scipio; accounts of its role in politics in the Hellenistic and Roman eras; there was even a bishopric there up until the 10th century or so. The only complication is that its name was actually Ilium (hence 'Iliad'): 'Troy' (or 'Troia') was an alternate name, and for one reason and another 'Troy' happened to become the more popular version in the Mediaeval period.
Here are a few of my older write-ups on the same theme:
