According to Maseter Yandel, Aegon had an interest in Westeros predating "the events that drove him to war." Aegon was noted to have spent time in Oldtown, the Arbor, and possibly even the Westerlands. This is a stark contrast to the Eastern focus of Aegon's Dragonstonian predecessors. Maester Yandel's context then goes on to show how Aegon's strength was a coveted resource. However, he would be provoked when the Storm King of the time wanted to use Aegon as a buffer between him and the surging Ironborn who held the Riverlands, with a functioning capital at the nearly completed Harrenhal. Agrilac (the Storm King) also proposed Aegon taking his daughter as Aegon's 3rd wife. When Aegon sent a counter proposal seeking much greater swaths of lands and a marriage of the daughter to his dear friend Orys Baratheon, the Storm King sent back the messenger's hands in a box. Yandel noted that, at the time, "the Westeros of Aegon's youth was divided quarrelsome kingdoms" and that "the two most beligerent" of these lay closest to Dragonstone. Finally, before declaring war, Aegon was seen to have spent 7 days in prayer in the castle sept--something he was not known to have done before.
In short, Aegon (1) was already interested in Westeros, (2) was recognized as a power, (3) was possibly bothered by the constant belligerence, and (4) was personally affronted by the Storm King.