What would be the most likely reason puritans decided to establish the massachusetts bay colony in 1620?

Because they were seeking freedom to practice their religion as they saw fit.

The Massachusetts Bay Colony received a charter from King Charles I of England.  They presented the settlement effort as a profit-making venture to the New World, rather than a religious enterprise.  But that was mainly to get the king's approval on their plans.  Charles I had not been favorably inclined to religious dissenters like the Puritans.  But in getting a charter from the king to go to settle in the New World, they were indeed seeking a place where they could practice their religion without interference.

There’s no picture, but i’ll give you a few of expeditions. lewis and clark began in 1804, louisiana purchase 1802, james town 1607