It's important to do it fast. So, kill Sardinia right at the start.
Then look for good ally opportunities like Venice, Portugal, Genoa or the likes. Navally strong middle powers with at least a bit of manpower behind them, that can interfere in the Mediterranean (Hansa or Holland won't help you much. Still better than someone like Bavaria ofc). Unally Sicily and punch them hard, annex with your mission.
Punch Naples right after, annex them as well with your special mission. As long as your navy + allied navies (but remember, allies are unreliable) have superiority over their & their allies navies, you should be able to do this relatively easy.
You should now be fairly strong, as long as Castille hasn't England or France as their ally, you should be fine, maybe even able to beat them one on one. PU'ing Castille would be incredibly strong, since you will get cores on inheritance. Same goes for Portugal.
You can however wait and look for other opportunities. Easy PU's are great. Especially if Bohemia is still HRE, you should be able to claim PU's over countries like Savoy or Milan. Another way to expand is the mentioned route into the Ottoman Empire, once you can beat them (blocking Bosporus with a superior fleet helps a ton here). Since you should get Epirus/Janina via the Annex Naples mission, you have a holy war casus belli and can therefore claim the relatively rich Greek and Turkish provinces for 1 infamy each.
If you follow the missions and then grab good opportunities, being the world's strongest power in 1500 should be certainly doable.