Everything has to be near perfect to accomplish this.
One of the things I did was start Jan 1, 1445, instead of Nov 11, 1444. This gives you Walachia as a vassal to start. Then it helps if Karaman doesn't ally with Aq Qoyunlu and Candar with Crimea. If Karaman allies the Mamluks, start over.
Ally and vassalize Ramadan, Dulkedir, and Hisn Kafya right away. You want HK, because that's one less pesky fort to siege when you're securing Eastern Anatolia, plus, they can help you eat the AQ in one war (assuming they aren't allied to Candar or Karaman). You should be able to finish this in the 1440s, after taking out Byzantium. It's sometimes better to wait on attacking the Romans to make sure HK gets vassalized, because every so often they ally Ajam, then get annexed in a war with the Qara Qoyunlu while you're taking out the Romans. Once these three are vassalized, start on Anizah, which isn't important itself, but once vassalized, it allows you to vassalize Medina. You have to be quick, because there's an event that annexes Medina to the Hejaz, and then you have to siege that damn fort. Vassalize Medina before conquering Karaman.
Conquer Candar and Karaman. If the AQ have allied one or both them, when you peace the AQ ONLY force them to release Syria, and NOTHING ELSE. That will give you a six year peace, and you can come back and wipe them out once you've cored all your conquests. The sooner you can finish the Eastern Anatolia Mission, the sooner you can finish the Levant mission.
Before your first war with the Mamluks, you need to force the AQ to release Syria, which will then gratefully agree to be your vassal. You should have fabricated claims on Antikya and Tarabulus-al-Sham. If the AQ weren't allied to Karaman or Candar, and you've completely conquered them, you can also fabricate a claim on Haleb. In the victory, give all of Fadl to Syria, and maybe Homs, depending on whether or not AQ has been conquered. That way you can send troops all the way down to Medina without being stopped by pesky Mamluk forts. Make sure NOT to give Haleb or Dimashq to Syria. Those are high value provinces for your economy and trade. Also force the Mamluks to free the Hejaz, which you will now be free to woo and vassalize. If you build up spies during the war (for siege bonuses), put claims on Sharqiya and Dumyat. Don't waste them on Syria or Palestine, as you will get those for free. You can sometimes pick up one or two of those provinces in the 2nd war while conquering the Levant, and then you can bypass Cairo to also siege Alexandria at the same time.
Having Medina and Hejaz as vassals makes the Conquest of the Hejaz mission so much easier, since you'll only have to take three more provinces.
You must fabricate Cyprus, so that after curb stomping the Mamluks, you can attack Cyprus, who is guaranteed by the Mamluks. White peace them, and you can attack the Mamluks again in five years, rather than 14. It takes 5 wars to annex all of Syria and Egypt, and that's with vassal feeding Syria.
Attack, conquer, and white peace Cyprus. You can now attack the Mamluks in the 1460s instead of the 1470s. By then you should have completed the securing of Eastern Anatolia mission, so you now you can complete the Conquest of the Levant mission. If you're lucky, you can do this two or three times before the Mamluks vassalize them. I wasn't lucky, as just after I conquered the Levant, Cyprus joined a coalition. Fighting them, the coalition, and the Mamluks, even though the Mamluks have no army or manpower at this point is a PITA. So I could only white peace sleaze once.
WHILE all of this is going on, you still need to conquer the rest of Greece, Serbia, Bosnia, Albania, the Italian Aegean, the Pontic and Italian Black Sea AND make Moldavia and Crimea marches. The Umera (aristocracy) gave me a submission mission for Moldavia, so that definitely helped.
Vassalizing Fezzan can be helpful, but is not necessary. When it's your vassal, the Mamluks concentrate on conquering it, rather than fighting your invasion, and you can often defeat the Mamluks more quickly this way. Because even a fully occupied Fezzan means little in terms of war score.
You should have nine or ten vassals by this point. Strong Duchies will mean you're only burning 3 or 4 Diplo monarch points. When you take Diplomatic ideas, that will drop by one, and Influence ideas will save you another.
Obviously, you want to take Administrative ideas first, because with all this conquest, you're doing a lot of coring. You want Diplomatic ideas next, to decrease province war score, so you can take more provinces, more quickly. Also, if you decide to break your truce, it's only a -3 stab, instead of -5 (and war exhaustion).
If the Umera offer you a vassalization of the Byzantines mission DO NOT TAKE IT. You can only complete the Conquest of Greece mission by owning all mainland Greece directly, not merely through a vassal. And they take forever to be able to diplo-annex. That will seriously hamper your conquest of the Balkans.