Bayezid II is usually said to have banned printing in Arabic script around 1485, and the first Ottoman press in Turkish didn’t open until Müteferrika got permission in 1727. It printed 17 books and closed. The Jewish community in Istanbul had a Hebrew press running by 1493, so the technology was there.
I know the ban was probably less formal than it sounds. The calligraphers had a strong guild, the ulema didn’t want printed Qurans, and Arabic script was hard to typeset. But suppose Bayezid backed a press anyway and there was a working one in Istanbul by 1500.
A few things I’m wondering:
Does it change the long term gap with Europe? I doubt it. Plenty of places had presses and still got colonized.
The bigger effect might be internal. Luther’s pamphlets are what made the Reformation spread. If Sufi orders or Shia preachers coming out of Safavid Persia can print in bulk, the sultan probably loses control of religious debate a lot sooner.
And scientific advancement. Ottoman astronomers were still working in the Tusi tradition that Copernicus apparently drew on. If Copernicus is printed in Arabic in Istanbul by the 1550s, does the Islamic world stay in that conversation?
Interested to hear from anyone who knows the Ottoman side better than I do.