If we set to onside the writings of Homer and instead focus on the archaeology and on Hittite written records that survive and which were contemporary with bronze age Troy, then we can build up a picture of the history of Troy from its founding until the time it became the Greek city of Ilium.
First, it is worth remembering that the city has been known by two different names - Ilium and Troy (and that the name 'Troy' refers more to the country than to the city itself).
Troy I: (c.3000-2500 BCE) Troy was settled at some time before 3000 BCE, it began life as a small village. It began life as a few stone and mudbrick houses with a very basic wall. Pottery and copper artefacts have been found from this early period .
Troy II: (c.2500-2250BCE) Troy doubles in size and acquires a citadel and became quite wealthy. It had a larger wall. It was quite wealthy and had economic connections with the Balkans and Afghanistan. A number of precious metals and finer items of pottery mark this period. It appears to have been sacked/destroyed twice and this is why Schliemann thought it might be Homeric Troy. It does however pre-date Mycenaean Greece by a considerable period of time.
Troy III-V: (c.2250-1800BCE) Troy over this period appears to have been smaller and less wealthy but still cosmopolitan enough to have imported Minoan pots. The archaeology of this period has been seriously compromised by Schliemann's cavalier approach to excavating it to get at Troy II.
Troy VI: (c.1800-1250BCE) Troy in its bronze age heyday. Troy expanded and had a population of at least 5,000. It had large stone walls. It appears to have traded both with the Anatolian and Mycenaean world. Its pottery styles, architectural designs, and burial practices were Anatolian rather than Mycenaean.
In 1280 BCE Hittite documents record a treaty with a King Alaksandu of Wilusa (thought to be an early form of the name that became the Greek Ilium). It indicates that the Hittites and the Wilusan people had enjoyed a relationship dating back three centuries by this time. Muwatalli II and Alaksandu of Wilusa respectively, invoked the water god, KASKAL_KUR, who was associated with an underground spring. Some scholars have linked this deity to underground springs found at Hisarlik, which would have supplied water to the citizens of the lower city.
Around 1250 BCE Hattusili III wrote to a king of Ahhiyawa, concerning the exploits of a renegade identified as Piyama-Radu against the Hittites and requests his extradition to face Hittite justice. In this letter Hattusili reminds Ahhiyawa that "Now as we have come to an agreement on Wilusa over which we went to war... " which suggests again that Wilusa (Troy) fell within the Hittite sphere of influence at that time.
It was destroyed in around 1250 BCE, almost certainly by an earthquake.
Troy VII (c.1250BCE-950BCE) Troy was quickly re-built, not quite so large but almost as grand as before. There is evidence that the population was restricted within the fortifications of the city - possibly for protection against raiders and other threats (perhaps the Mycenaeans).
Troy VIIa was destroyed, probably sacked by invaders in around 1180BCE. Bronze age arrow heads and corpses of people who had died violently, as well as signs of deliberate arson were contemporary with this event.
This sacking is the only archaeological evidence for a major siege ending in a catastrophic sacking that would come close to something described by Homer. By this time the Mycenaeans themselves were in serious decline and so this has raised the question as to whether the 1180 sacking was the work of Homer's Mycenaean heroes or the work of other invaders (possibly from south eastern Europe).
Troy VIIb - Troy was rebuilt and continued to produce the characteristic Anatolian Grayware pottery that is also found in Troy VIIa. Towards the end of this period a new style of pottery Buckelkeramik which is more characteristic of south eastern Europe increasingly appears. Trou VIIb was finally destroying in a fire in around 950 BCE. A Luwian seal has been found dated to this period which suggests at least some native Anatolian people remained in the city. The only written language found at Troy from the bronze age or early iron age is this seal. At present, it remains the only language that we know for sure was in use in bronze age Troy.
Dark Age Troy: (950-750BCE) After 950 BCE Troy was largely abandoned & the area was very sparsely populated.
Troy VIII: In 750 BCE Attic-Ionic Greeks settled Troy and founded the Greek city of Ilium on the site. The new city featured a prominent temple of Athena.
So, there is nothing in the archaeology that fits that well with Homer's story. The best candidate is the sacking of around 1180 BCE. However, this occurs at a time when the Mycenaean world was itself in turmoil / terminal decline, which makes it slightly problematic.