Did Jews build ships?  Certainly the most famous ship builder from the Bible was Noah, but there is no indication that ship building was a common practice at his time.  It didn't seem to be his fulltime occupation.

The books of Job (some consider the earliest written book), Exodus, Numbers, Judges, 1 Kings (Solomon) Psalms and Isaiah include references to boats and ships, so the answer is yes.  Ships were built and they were around.  Solomon had a Navy.  So we can't rule out the possiblity of Jews boarding ships and sailing some where.

1 Nephi 17 says that Nephi built his ship on the sea of Irreantum (which nobody knows where that is) using tools he needed to construct out of ore, with the help of a bellows he made out of animal skins (a practice that was used in Egypt and China).  The ship was made of timbers, according to 1 Nephi, also a common practice.  However, Nephi said he made it not in the manner men, but the manner which God showed him.  What that was is unknown.

1 Nephi 18 describes their perilous journey eastward when they arrived at the Promised Land.  The land included cows, oxen, donkey, horses, goats and wild animals, and lots of ore, such as gold, silver and copper.

So Jews of that day (600 BC) would have the knowledge to build ships, but whether those ships could withstand the length of the journey is unknown.  Columbus in 1492, sailed on three well-crafted Italian ships, built with 1500 more years of technology and had a hard time.  Pilgrims in the 1600s nearly killed themselves on ships.

NOTE: Cows, oxen and donkey don't run wild.  Horses and goats do.

NOTE: Most copper mines are found in Arizona, Alaska, Montana and Utah.  Not on the eastern seaboard of the United States.  Silver could be found in Mexico.