The thing with the Ottomans is that I lack allies that would go to war against them. France is friends with Ottomans and I don't have any other allies atm. Russia doesn't like me for some reason. And I don't think I can take Ottomans by myself. Their army is 3 times the size of mine.
For Roman Empire you need all of Balkans, Greece, Anatolia and Mashriq. Just clicking once on all these provinces would take me 15 minutes.
You have both Admin and Influence ideas and you are Italy, so monarch points won't be an issue.
They might have three times the army, but so do Ming when you first invade them. However, your choice of Offensive idea group is wrong. Instead, you want either Defensive, Quality or Quantity. You can probably skip Quantity as, by now, you should probably have enough income to plant a +1 forcelimit building everywhere. That's 30+ forcelimits hiding right there.
Quality is a solid choice because it provides you with +25 % infantry combat ability from the very first idea (10 from quality, 15 from italy). However, to skip the morale bonus from Defensive, you need a healthy influx of reinforcements in large battles, luckily you have +10 % from Plutocratic.
Provided the Ottomans have no other significant allies (if you declare some dummy war into which you can drag France into), your setup should revolve around two things:
First, you want to lock down your provinces you want to defend: forts in mountains and hills so their armies can't enter Italy. If you want to defend in Maghreb, your fort is in the wrong spot - the original position, the one you deleted, is superior (one province South West from current fort).
Second, you want to have a navy that can beat the ottoman navy: 30 heavies, 90 galleys, an admiral. You probably will need to do this only once, since the AI doesn't prioritize navies that much, so feel free to go way above the forcelimit and cut down after the first war (but not by more than 30 %).
The first war will take a long time, so feel free to take time to prepare. It might be useful to drill up armies to max, but it's not mandatory. The target province you should declare for is either Corfu or Naxos (can't see if you control Crete or not), one of the islands you can fabricate on. Naxos is a better choice because it doesn't have a fort and is in Aegean sea. Once you siege it down, prevent ottoman armies from reclaiming it. This leaves the Ottomans with no choice but to go for your lands. The most likely point of their attempts is Friuli or Maghreb, the better option is Friuli (so try getting passage from Austria once the war starts to force this).
What you need to do is stackwipe around a third of their troops, I presume that's around 100K. For that, you'll need 20-30k more troops (to have around 120k). The first few battles will be the worst and probably won't be stackwipes, but if you do this by defending your forts in the hills/mountains, you shouldn't lose more than 40K men. This leaves you with 80K manpower to rout their returning armies in the plains of Hungary and siege down a few forts in Greece (including Constantinople). Keep your army in two stacks of 60K (or 3 of 40K) and stackwipe their returning siege armies. Once they have around 180-200K, make your way (fort by fort) though Romania and Bulgaria to Constantinople.
During this time, your navy should keep defending your sieged down target province and preventing naval transports from reaching your lands. Once your armies reach Constantinople, the navy should be split between Sea of Marmara and Aegean. Feel free to spend 100 mil points on breaching the walls on these two forts, but take them 1 by 1, not two simultaneously.
If you siege down Edirne and Constantinople, you're in the clear. Even if the Ottomans still have 100K troops in Greece you should be able to rout them and stackwipe them.
By this point, you should be sitting at solid zero manpower, while the Ottomans will have around 50k manpower and around 180-200 K men (of which 30-50K are newly built units). But they can't reach you. Your aim is to siege down enough forts in Greece (with zero manpower) to get to around 60 % warscore. Take Constantinople, Edirne and/or, if possible, attack Ragusa while ottomans can't defend them and create a 1-province corridor that links Dalmatia, Ragusa and Montenegro with Edirne and Constantinople. It might also be worth it to sacrifice 10% warscore and get annul treaties with France.
Your next war should be vs. Mamluks (vassalize if possible) to take Upper Egypt and for your next war vs Ottomans you should really work on your diplomacy
EDIT:
Composition suggestions:
Combat width: 32
Army comp: 30/2/28
Total number of armies: 2 (120k)
Naval combat width: 33 (coastal) +3 per admiral maneuver pip.
Heavy ship width: 3
Galley width: 1
Total width (presuming 1 manevuer pip): 36
Naval comp: 8 heavies (24 width), 12 galleys
Total number of fleets: 4 (32 heavies, 48 galleys), 30-40 extra light ships or galleys.
