According to /u/Ahhuatl, this happened in the Christian world - people wondered why the infallible word of God had not spoken at all about all the millions of people and their cities, and why these people did not know anything about Christianity when the Bible claims that the word of god had been made known to all the peoples of the earth.
Did any such debate happen in the Islamic world?
To the best of my knowledge, no, there is no evidence of such a debate.
The New World began to appear in Ottoman geographical sources relatively quickly after its initial discovery. Its first appearance was in Piri Reis' world map of 1513, which was based on western sources. The existence of the New World doesn't seem to have drawn a great deal of controversy. The first major work in Ottoman Turkish discussing the topic was the Târîh-i Hind-i Garbî, composed sometime between 1580 and 1582 and presented to Murad III. The bulk of the book consisted of translations from (the Italian versions of) several Spanish accounts of the New World. The introduction included a brief discussion of cosmology and geography. It seems as though the New World was significant to the Ottomans mainly in terms of its relation to geographical knowledge, and not theological questions.
The scholar Kâtib Çelebi (d. 1658) mentioned the discovery of the New World in his treatise on contemporary religious disputes in totally casual terms without mentioning any controversies associated with it.
It may be that the Ottomans, having had no direct contact with the Native Americans, simply felt no need to address them and focused their intellectual energies on the more immediate debates and controversies which were cropping up in the sixteenth and seventeenth centuries.
Giancarlo Casale, The Ottoman Age of Exploration (Oxford University Press, 2010), 25, 160.
Thomas D. Goodrich, "Tarih-i Hind-i Garbi: An Ottoman Book on the New World." Journal of the American Oriental Society 107 (1987): 317-319.
Kâtib Çelebi, Mîzânü'l-Hakk fî İhtiyârü'l-Ahakk, 34.