If you’ve read The History of the Decline and Fall of the Roman Empire–and, you know, who hasn’t–then you may know that Edward Gibbon marks July 27, 1299, as the date of the founding of the Ottoman Empire. It was on this date, according to Gibbon, that Osman I (d. 1326), the Ottomans’ founder and namesake, led his fighters (it would be exaggerating to call it an “army” at this point) on an invasion (“raid” might be the better term) of Nicomedia, which was under Byzantine control at the time (and would remain so until 1337). This may have been the first Ottoman raid into Byzantine territory.
Source: Today (sort of) in Middle Eastern/European history: the Ottomans get started (1299, or 1302)