Yes, they believe there was a family from another tribe of Israel that had a civilization that eventually wiped itself out in the Americas. They enjoy guessing where it was, and how large they had gotten. The term Mormon comes from the historian that compiler the history of his people and had his son preserve the record before he died. Hence the Book of Mormon. It is believed that Joseph Smith found and translated this book by divine means, and then founded his faith based on what he had learned from it, both the writings and the divine help to translate.

The problem is the period in history that it happened had several civilizations wiped out, and the known origin is a shrug of the shoulder.

There were also several trade groups that were part of the Americas. Hence relatives of potatoes found in New Zealand, and chicken bones found in Chile. It is difficult to prove totally, because the civilizations enjoyed destroying each other. Basically, the general thought is that there have been several groups that have entered the Americas, but no one knows all of them and only have hints at a few.