As the Portuguese gradually extended their explorations and trade ever further south along Africa's Atlantic coast during the 15th century they needed a larger and more advanced ship for their long oceanic adventures. Gradually, they developed the carrack from a fusion and modification of aspects of the ship types they knew operating in both the Atlantic and Mediterranean and a new, more advanced form of sail rigging that allowed much improved sailing characteristics in the heavy winds and waves of the Atlantic ocean.
So this was a gradual process. Earlier Carracks used clinker planking rather than carvel planking. There was no first carrack or definite date of the first carrack. Many older carvel were modified into carracks by adding a foresail, a square mainsail, and a lateen mizzen. However, most left off the high forecastle and the sternplace. These were called caravela redonda (not to be confused with the Portugese fighting ship of the 16th cenury of the same name). The Niña was a caravela redonda.
The Portuguese continued to develop the Carrack well after it was considered the main beast of burden of the Age of Exploration:
A new sail, the topsail emerged above the mainsail in the late 15th Century, first as a small yard and sail on the flagstaff rising from the top, then as a full-sized sail on its own mast attached to the mainmast. Later, also the foremast got its topsail.
By the end of the reign of the carrack, a third sail, the topgallant sail had appeared in some ships above the topsail in its topgallant mast.
So the carrack continued to develop throughout the 15th century and even into the mid-16th century. The first "carrack" was probably a modified caravel. We do not know for sure who first came up with the idea, if there was but one man; if ever it has been known, it has long since been lost to history.