You're right in that salt has been a staple basically worldwide due to its preservative abilities, and we have evidence that salt was collected as early as the neolithic era. In terms of when salt went from being primarily a preservative to primarily a seasoning would have been when other methods of preservation began taking hold. Up until the advent of canning in the early 19th century, one of the primary forms of meat preservation was salted meat. After the advent of large-scale canning, salted meat became less of a necessity.

In terms of pepper, according to Davidson and Saberi (p. 178), there's evidence of pepper being grown in India as far back as 2000 BCE, and evidence of black pepper in Egypt as early as 1200 BCE (Fitzgerald, p.88). After the conquest of Egypt by Rome in 30 BCE, black pepper became fairly ubiquitous in the empire. According to the greek geographer Strabo, the roman empire annually sent a fleet of 120 ships to India and back for trade, where black pepper would have been among. Given the expansion of the Roman empire, black pepper quickly made its way across a wider geographical area and was much appreciated by everyone. Even Pliny the Elder mentions it in Natural History (12.14). The popularity of pepper persisted through the middle ages, although it eventually became a luxury good due to the high cost of importation from southeast asia. Of course, it would have been included in the spice trade from Europe to India. As the greater world colonization by the European powers took place, the quantity of trade between the east and west brought more and more spices, pepper included, into Europe, lowering the price and enabling the masses access to it, and from that point it became a more ubiquitous, everyday spice.

In addition, /u/Frescanation goes into greater depth here