Is it possible that the Romans stumbled upon the Americas?

Recently I read a book about how there is a lot of evidence suggesting that the Romans might have stumbled upon America. Things such as coins, sculptures, inscriptions, and even a ship have all been found in North and South America. I know there is no recorded evidence for a Roman discovery of the new world but it might have been possible that the Romans had no idea where they were. Some of the coins had been found buried in mounds that date back to 490 BCE and 800 CE. In 1886 the remains of a Roman looking ship were found in Gavelston, Texas, it's too hard to tell definitively but ship experts say it was possible for late period Roman ships to sail the atlantic. I find this subject rather interesting so I am asking this question out of curiosity.