And I, Nephi, did build a temple; and I did construct it after the manner of the temple of Solomon save it were not built of so many precious things; for they were not to be found upon the land, wherefore, it could not be built like unto Solomon’s temple. But the manner of the construction was like unto the temple of Solomon; and the workmanship thereof was exceedingly fine.
And it came to pass that I, Nephi, did cause my people to be industrious, and to labor with their hands. 2 Nephi 5:16-17
Building a temple is hard work and requires lots of people. Ask King Solomon.
King Solomon conscripted laborers from all Israel—thirty thousand men. He sent them off to Lebanon in shifts of ten thousand a month, so that they spent one month in Lebanon and two months at home. Adoniram was in charge of the forced labor. Solomon had seventy thousand carriers and eighty thousand stonecutters in the hills, as well as thirty-three hundred foremen who supervised the project and directed the workers. 1 Kings 5:13-16
It took Solomon 13 years to build this temple with 30,000 men in shifts of 10,000 a month. The workmanship was so massive, the foundation is still there today.
Where is the foundation of that temple in America today? We don't know. Nephi (or the writer Joseph Smith) excuses the workmanship of that former temple saying "well it wasn't as good as Solomon's, but it was okay." Obviously it blew away.
How many people came over with Nephi? Enough to build a temple? 2 Nephi 5 was written, according to the Book of Mormon, in 588-570 BC, the same time period as Nephi sailed to the Americas. The ships could not carry very many people in those days. The Mayflower carried 120 people in 1620 AD. Columbus brought, it is believed, about 40-80 on each ship in 1492 AD. So in 570 BC, there could not be more than 100 people that came over in a ship during that time. But remember, those groups split up, so Nephi only had a percentage of that 100. With repopulation and children being born, Nephi would not have any more than 100 in his tribe if those kids grew up to be temple-building teenagers. Not enough to build a massive structure.
Would God want a second temple built? Absolutely not. When Israel split after Solomon and a second temple was built in Samaria, God was not pleased, especially when it started to worship Baal and other gods. God's direction was for one king to build one temple in one location. That was Solomon and the place was where Abraham was willing to offer his son as a sacrifice. That place had meaning. Also when God builds a temple he gives very specific directions/blueprints as to how it should be made. God gave no direction to Nephi as to the specifications of this temple.