Towns like Boston and New Amsterdam grew quickly into large cities because

Cities like Boston and New Amsterdam have grown rapidly to large cities because of the large number of English immigrants.

Explanation:

Boston became big due to the large number of immigrants, mainly English. This caused the city to expand and become a great cultural and economic center, since trade was something very dynamic, diverse and productive in this region.

New Amsterdam, on the other hand, did not have as many immigrants when it was under Dutch rule. That's because Holland was economically well, at that time, so few Dutch people were willing to be colonists in the Americas. However, this region had a strong trade, mainly for furs. In relation to immigration, this scenario changed when this territory came to be dominated by England, which attracted a large number of immigrants.

because the early people found out about it.