Once again my man; if you want to understand why the Ottomans are so powerful, you need to read about the Ottoman Sultanate under the rulership of Beyazit, because this is the point of divergence.
Don't try to be condescending. I read about the Ottoman Empire and have an idea about its military capacities.
At the time of the Battle of Ankara in 1402, the Timurids and the Ottomans both fielded the two largest armies in the Islamic World (accounting of course for vassals). The Ottoman army of the time numbered around 100,000 soldiers according to some estimates, with around 15-20,000 Janissaries as they controlleld a substantial amount of Balkan territory.
It did not have 15 - 20K Janissary, just under 8K of them and they were the only high-quality troops. Admittedly, at that time 8K of a high-quality infantry was a considerable force but it was not adequate for the grandiose conquest you fantasized.
In OTL the Ottomans had been expanding into the areas with a high degree of a power vacuum (the Balkans) and even then expansion was quite slow in most cases.
In the case of the Mamluk Egypt they won (after losing the 1st war) due to a technical superiority of infantry with the firearms over the cavalry with the bows (Mamluks). In the Eastern direction they had been expanding mostly when Persia was weak but Nader Shah was defeating them.
At the time of Bayazit the Ottomans did not even have
Kapıkulu Süvarileri ("
Household Slave Cavalry") introduced by Mehmed II. The Yaya units (created in the early XIV and abolished in 1582) had been irregulars of a low quality and not very good in the field or at the sieges. Sipahi and Akinci were typical irregular cavalry.
As for Ankara and the numbers involved, it is rather hard to believe all these huge numbers when 500 of the Serbian knights had been playing such a prominent role in the event.
In other words, Ankara or not, the Ottoman armies of the pre-modern times were not excessively big and their high-quality part was even smaller. An idea that they'd just keep growing with a growth of population is, of course, "interesting" but here goes the problem: by 1500 population of the Ottoman Empire was approximately 11M, the HRE - 16M, France - 15M, Spain - 8.5M, the PLC - 7.5M. In other words, population of only the
main Ottoman opponents was approximately 4.5 times grater than one of the Ottoman state and, following your idea about the direct relation between the population and army size, the Ottomans would be simply squashed by the much greater numbers. Of course, in a real life this dependency did not exist until the age of the universal conscription and your speculations simply do not make too much sense.
Anyway, in the time when the reported numbers became more reliable sizes of the Ottoman armies suddenly began dwindling regardless a considerable growth of population. By 1800 population of the Ottoman empire was approximately 26M but in the wars of the late XVIII - early XIX size of the Ottoman armies is seemingly in the low 100Ks and by 1877 it is under 300K.