Here's some "hard evidence" about SOME (not necessarily THE) Jews who rafted from the Old World to the New World, as depicted generally in the Book of Mormon. The "hard evidence" is a stone inscription in ancient Hebrew located in Bat Creek Mound #3, Loudon County, Tennessee, and dating to Book of Mormon times. See my oft-posted quotation from Cyrus Gordon on the above dig, which was carbon-14 and scriptographically dated to about 100 A.D.
There are two *major* problems with using the Bat Creek findings to validate the Book of Mormon. First, and most importantly, the bracelets found in the same burial mound date to the 18-19th century--meaning that the stone probably didn't find its way into the mound until then (so it could have easily been brought over after Columbus).
"Recent tests by our Conservation Laboratory on the brass bracelets found in the same grave definitely established that they are 18-19th century trade goods and do not have the chemical composition of brass of the Roman or early Semitic periods." (Statement by the Smithsonian Institution, November 24, 1971)
Second, Gordon himself stated that the script relates to Jewish coins that date to between 70 A.D. and 135 A.D. so the stone couldn't have been brought to America until after then. Last time I checked, the Book of Mormon only speaks of people coming to America more than 600 years before this.