After examining several sources, it seems that 1299 is quite arbitrary. One source says it was chosen by Sultan Abdul Hamid (1876-1909) as that's when the Seljuk Sultan was kidnapped by the Mongols, giving the beyliks in Anatolia effective independence. But according to this same source, that event happened in January of 1300, not 1299. (https://www.dailysabah.com/arts/portrait/mighty-sovereigns-of-ottoman-throne-sultan-osman-i)
In her book, Osman's Dream, historian Caroline Finkel claims that the year is cited as the birth of the empire because of a rare event where the Christian and Muslim calendars both experienced a century change at the same time. This seems quite weird to me. It is a rare event, but it has nothing to do with the Ottomans, so why is that so important? (Osman's Dream by Caroline Finkel, p. 2)
To me, 1280 and 1301 both seem like equally good years to define as the start of the Ottoman Empire. 1280 became that's when Osman's father, Ertuğrul, died, leaving Osman the ruler of his small beylik. But if you insist, as Ekinci (historian behind the article above) seems to do, that the Ottomans could not have started before gaining independence from the Sultanate of Rûm, then 1301 seems like a perfectly acceptable option. Because in 1301, the Battle of Bapheus happened, fought between the Ottomans and the Byzantines. While not super important, it was important enough for Byzantine sources to write of the battle. That indicates, to me, that Osman had achieved a relative degree of independence from Rûm, as I don't think that the Sultan of Rûm would've been to happy with one of his subjects making trouble with the Byzantines. Ekinci claims that Osman was often sent as a representative of his father's while his father was still alive. If that's true, then I can only imagine that Osman had at least some sort of amicable relationship with Rûm. Rûm was, at this time, declining, but it was still the dominant force in Anatolia, so I can't imagine they'd be too happy with Osman making trouble with the Byzantines. Again, that's just my assumption and could very easily be wrong.
In any case, 1299 holds absolutely no historical significance in the history of the Ottomans, Anatolia, or the world. The event cited by Ekinci happened in 1300, not 1299, and the alignment of the Muslim and Christian calendars is interesting, but ultimately extremely unimportant in Ottoman history. It seems, to me, that both 1280 and 1301 are much more natural years to pick as the start of the Ottomans, and I personally lean more towards 1301.
Thanks for reading, and thanks in advance for any insights into this issue.
According to traditional sources Ottomans under Osman Bey captured the town of Karacahisar between 1286 and 1291 and in 1299 he had the Friday Khutba read under his name in this town [1]. For those that don’t know Friday Khutba is a prayer that is read by the imam during Friday prayer, and it is read under the name of the sovereign. Khutbas before that time were read under Seljuk sultans name. This was a sign of sovereignty and the main reason it is usually assumed that the Ottomans became independent in 1299.
Now let’s talk about why the dates you mentioned would not be accurate.
In 1280 it was clear that the Ottomans still paid lip service to the Sultan of Konya. After Osmans conquest of Karacahisar in late 1280s or early 1290s, Osman reported his conquests to the sultan, and sent him a share of the tribute. In response Sultan Alaaeddin III granted the conquered land to Osman, and sent him horse hair banners (tug) [2]. Tug was the sign of governorship or beylik, a clear ceremonial artifact that shows a hierarchy between Sultan Aladdin and Osman.
1301 would also be invalid because Bapheus happened in 1302, however you aren’t alone in placing the foundation date of the Ottomans after the Battle of Bapheous. One of the greatest Ottoman historians, Halil Inalcik also argued that the Ottomans became independent practically after Bapheous, so that would not be a wrong claim per se.
Sources
[1] İnalcık, Halil (Ekim 2017b), Osmanlı İmparatorluǧu Klasik Çaǧ (1300-1600), Ruşen Sezer, çev. (24.baskı bas.), İstanbul
[2] Öztuna, Yılmaz (1988). Mawsūʻat tārīkh al-Imbarāṭūrīyah al-ʻUthmānīyah al-siyāsī wa-al-ʻaskarī wa-al-ḥaḍārī