I am not contradicting you about the ancient African voyages. I am merely pointing out the issues with strictly sailing and combined sailing/rowing ships of the time were not due to technology, but the navigational technology, logistics, ignorance of the currents and lack of purpose for a trans-Atlantic voyage.
The question is what ship characteristics were required for trans-Atlantic voyages. These are a strong, watertight hull, reasonable sails, preferably with some upwind ability, decent maneuverability, a relatively large load capacity for burden, and a skilled and brave crew. These are available in the west by the Punic wars. Now, provide them with a compelling reason to sail away from the known world into the unknown.