WIth Ottomans annexing Egypt before 1519 is not hard at all. Even with 3-4 wars it isn't that hard as long as you pay close attention. First war at about 1450, ideally you will grab the non-Mameluk Syrian core first and release Syria. You take Gaza and the other province to cut off Palestine/Syria from Egypt, use the rest of war score to either grab Jerusalem and feed provinces to Syria or just grab Alexandria even without the claim. Simply because in next war everything in Levant will be super cheap to grab as it will count as overseas. So second war is launched with conquer Egypt (in the meantime fabricate claims on Palestinian provinces because you will lose the conquer Levant mission claims if you feed anything to Syria and besides you want the conquer Egypt mission) and you return the remaining Syrian cores to your vassal, grab the claims you fabricated in Palestine (both of these should be dirt cheap in WS) and use the rest of WS to ideally get a land connection from Gaza to Alexandria by taking the Nile delta provinces. It should be doable to annex within 50 years of start without any major exploits. And 75 is easy to achieve without much stress, matching historical annexation date. You just need to plan to start wars as soon as truce timer ends and everything after the first war is trivial and mostly just waiting for sieges to complete.
The Mamluks is just a part of the huge conquests the Ottomans did in more or less a century. You also have to conquer Iraq, Hungary, North Africa, Arabia and Crimea.