The roman naval technology was really not very advanced. But perhaps we overestimate this fact. The keel trended to break in rough sea. That was one reason why roman ships usually just sailed from Mai to August in the Mediterrenean Sea. Just bigger ships were a bit more robust and started to sail already in March. But they had the same construction flaw, and usually prefered to sail near to the coast. These are no good terms to cross the Atlantic.
However, roman ships made it to India, the Canaries and the islands north of Scotland. So I would not fully exclude, that it could happen. But surely not the route Columbus used. Other than Columbus the romans believed, that the size of the earth is 40.000 km. So they would not try to cross the Atlantic.
But I see 2 opportunities, how it could happen by accident:
1. If Agricola conquers entire Caledonia and the islands north of it, the romans might meet local fishermen, which tell them about a land in the north (Iceland). The romans believe it is the legendary Thule and start an expedition under good weather conditions. So they use the route the Vikings used. Again, the Vikings had the better ships. But perhaps the people on the northern islands have better ships, too?
2. The romans explore the west african coast down to South Africa. On their way back, they land in Brazil. This is not very unlikely, if they just do it often enough. Because ocean drift and wind often leads from South Africa to Brazil. The Portuguese used this route regulary on their way back home.
The problem is, why should the romans be interested in West- and South Africa at all? We discussed this already in this other thread and the conclusion was, that the trade at the east african coast was more than enough from a roman point of view.
And finally, whatever route the romans take. If they do not find the gold in Mid-America, they would loose interest pretty soon, like the Vikings.