Well, Diu is an absolute necessity, yes, but it's not enough because all of the reasons they lost at Diu are reasons this is impossible.
1) India is as close by sea to Lisbon as it is to Istanbul. The Ottomans' main naval effort in this period was non-oceangoing ships for control of the Eastern Med. An Indian ocean fleet would have to be an entirely separate affair, which brings us to
2) They don't care. Oh, sure, it would be
nice to keep control of the routes to India, but the effort required to build an oceangoing Red Sea fleet and then maintain control over sealanes that bypass Arabia by a couple of thousand miles would be totally incommensurate with the reward. And even if they try, we get
3) At sea, the Europeans are just better. The Ottoman Empire had some amazing, world-beating tools in the early modern era, like logistics to make Caesar weep and the artillery train from Hell. None of this is particularly applicable to shipbuilding or naval strategy (try and put
this sucker on a galley, see where that gets you), and the Ottomans don't have issues with this. Ottoman control of the sea, even the Eastern Med, was sketchy at best, and they didn't care, because it wasn't an issue to their general strategic outlay.
Short version: The Ottomans aren't doing it. Now, "Some type of Muslims keep Europeans out of the Indian Ocean for a couple of centuries" might just be plausible (although there's no real contenders for the title - bigger, angrier, earlier Oman, maybe?) but the Ottomans owning it for three centuries? Not going to happen.