The Devanagari scripts, as I understand it, have lots and lots of variants where letters go under or over or around the next letter, plus digraphs (combination forms), and so on.
The Arabic based North Indian scripts (e.g. for Urdu) presumably have all the problems that Arabic has with multiple letter forms.
That makes India a bad place to start printing with movable type. As various people have pointed out, Arabic (and thus, I assume, the Persianate forms used in India) certainly can be printed and the difficulties are often overstated, but I would think that it would make it trickier to start printing there.
Also, what kind of press exists in India that would make a good starting point for a printing press? Europe had olive presses (iirc), which they adapted. I have no clue what India had that way, or hadn't, but if you have to invent BOTH the type AND the press at once, it's going to be a much, much bigger hurdle.
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Also, you need a cheap material to print ON. When does paper appear in India. If you need three separate independent inventions to get printing somewhere, it just isn't going to happen.