That's not the reason. The European explorers didn't come to NA to colonize...there was no profit in colonization yet. They were primarily looking for routes to China that didn't require sailing around either of the horns...the fabled "northwest passage" Once they found this side of the planet, they started looking for valuable goods that could be exported back to Europe. Gold was at the top of their wish list, but there was soon a very brisk--and very profitable--trade in fish and crops never before seen in Europe--corn and tobacco among others. And contrary to popular belief, American colonies were founded on economics, not quests for religious freedom.
Most of the European--mostly French and Spanish, but some English too--exploration of what's now the US took place before 1600, but while they got busy colonizing what became Canada as early as the 1400s,, colonization of what became the US didn't begin in earnest till 1600. There was a little bit before then...St. Augustine FL was the earliest European settlement, in 1565...followed by Jamestown in 1607. The Mayflower was actually headed for Jamestown, which was well established by 1620, but they ran into weather that forced it northward to land on Cape Cod. It was September and by then winter was hard approaching, so they didn't have much choice but to stay there. Rhode Island and Connecticut were founded in 1636...Delaware in 1638...and y'all can do your own research find out when the rest of the colonies were first settled.
This HAS been fun...sure beats the socks off another toilet thread!