Yes in the sense that had the West African 'States/Tribes' not had slaves to sell, the trade would not have been created.
Slaves were bought, becuase basically those people in Africa had nothing else to trade. West African trade was reliant on slavery. The European traders would have been much happier trading spices, because the profits were higher. Slavery filled a gap, the traders would take European manufactured goods to Africa, sell them for slaves, ship the slaves to the West Indies, and then ship mollasses, sugar, and cotton to Europe, these last were the big profit makers.
That made good trade, but the European traders would have made much higher profits if Africa could have supplied exotic spices, which commanded super high prices. These could have been shipped straight back to Europe, load up with manufactured goods and go and buy a boat load of spices from Africa. No long voyages across the Atlantic, only the treacherous Bay of Biscay to navigate, which they still had to do when they crossed the Atlantic from the Carribean.
Slavery had all but died out in Europe, and it was deemed unchristian. The first explorers along the African coast were looking for profit, they had goods to sell, and needed to exchange them for other goods, the Africans dealt in slaves as their predominant industry. In Africa it was regarded as part of life. In that sense yes the Africans created the slave trade, also because the Africans were not Christian, they could be bought and sold, by Christians.