Perhaps Bill Bryson says it best (and most succinctly) in his book, At Home. “They didn’t. They didn’t know how.”
The original European colonists who settled in what became the thirteen American colonies were English. They settled in Virginia and Massachusetts in the early decades of the seventeenth century and later in other colonies. They built the sort of houses they knew from home: wooden frame houses or brick. Wood was plentiful in the colonies. Brick was not difficult to make.
(Even earlier than the English were the Spanish, who settled Florida in the 1500s. They did not build log cabins either.)
The first log cabins came with Scandinavian immigrants to the colony of New Sweden (around Delaware & New Jersey) in 1638. They built traditional Scandinavian-style homes like this one:
Gradually the log cabin caught on with other ethnic groups and became the first house European settlers would build on the woodland frontier. (In the Great Plains region where there were few large trees, sod became the material used for the first house.)