The Romans, or rather the Greeks, because in Roman times the vast majority of mariners were Greek, and possibly Phoenician, could have crossed the Atlantic. Technically. The classical world had extensive long distance maritime trade; ships went from Egypt to India and back routinely. They also had ships larger that the ships used by Columbus. They had lateen sails. But --

• They didn't know the Americas were there. As far as they knew, there was no land between Europe and Africa and Asia, and they knew perfectly well how big the Earth was. (This was the reason Columbus had so much trouble getting the funds for his expedition; he wanted to sail west to Asia and he insisted that the Earth was a lot smaller and Asia a lot bigger; all professional geographers knew that his numbers were wrong.)

• They didn't know how to navigate in open sea, or at least they didn't like it, not one bit; but that was a cultural and not a technical limitation. They could have learned quickly if they had a reason to; but they didn't, because in the Mediterranean they didn't have to.

• They also had no idea of the volta do mar, which makes returning from the Americas quite iffy. To learn this they would have needed to colonize the Canary Islands and the Azores, which they didn't although they knew perfectly well were they were.

Basically, the navigation was not a show-stopping problem.

The fundamental problem was that the Romans were simply not explorers; the genius of the Romans was in administration, in justice, in engineering, in matters military. Exploring was not in their world-view. All the great explorers of the Ancient world had been Greek or Phoenician -- Pytheas, Simmias, Megasthenes, Hanno, Himilco and so on. Not one Roman among them.

They also lacked any incentive to cross the ocean in search of land. There was land aplenty at hand, for example the vast plains of Ukraine, well within the Roman sphere of influence. When they didn't bother to colonize the Ukrainian plains, of which they knew, from where they imported wheat, it's useless to speculate about ocean-crossing exploration.

The Romans, or rather the Greeks, because in Roman times the vast majority of mariners were Greek, and possibly Phoenician, could have crossed the Atlantic. Technically. The classical world had extensive long distance maritime trade; ships went from Egypt to India and back routinely. They also had ships larger that the ships used by Columbus. They had lateen sails. But --

• They didn't know the Americas were there. As far as they knew, there was no land between Europe and Africa and Asia, and they knew perfectly well how big the Earth was. (This was the reason Columbus had so much trouble getting the funds for his expedition; he wanted to sail west to Asia and he insisted that the Earth was a lot smaller and Asia a lot bigger; all professional geographers knew that his numbers were wrong.)

• They didn't know how to navigate in open sea, or at least they didn't like it, not one bit; but that was a cultural and not a technical limitation. They could have learned quickly if they had a reason to; but they didn't, because in the Mediterranean they didn't have to.

• They also had no idea of the volta do mar, which makes returning from the Americas quite iffy. To learn this they would have needed to colonize the Canary Islands and the Azores, which they didn't although they knew perfectly well they were there.

Basically, the navigation was not a show-stopping problem.

The fundamental problem was that the Romans were simply not explorers; the genius of the Romans was in administration, in justice, in engineering, in matters military. Exploring was not in their world-view. All the great explorers of the Ancient world had been Greek or Phoenician -- Pytheas, Simmias, Megasthenes, Hanno, Himilco and so on. Not one Roman among them.

They also lacked any incentive to cross the ocean in search of land. There was land aplenty at hand, for example the vast plains of Ukraine, well within the Roman sphere of influence. When they didn't bother to colonize the Ukrainian plains, of which they knew, from where they imported wheat, it's useless to speculate about ocean-crossing exploration.