Who were the first people to start wrapping?

Answer 1

People giving gifts; ancient Egyptians when mummifying wrapped their kings' bodies,

but I doubt this is the question intended but distorted by a spelling error, so:

If the question is misspelled and wrap should be rap, perhaps one might think of early Bob Dylan's talking resistance prose, and even Alan "Blind Owl" Wilson, from the late '60s "Canned Heat", especially in his fast and powerful "Boogie Music" in which he elucidates the importance of blues-based "boogie" music as a a nearly politically fueled polemic by speaking through the rhythm of the music without using melody to express himself.

In short, these are some of the recent roots of what became to be known decades later as rap music. Many others outside this writer's knowledge were also precursors of what became rap. Perhaps one could also point to any chanting forms of music by indigenous peoples around the globe long before written history.