If they were Christian documents, you’d expect them to use the term Christ or Jesus. Rather, they use the term Creator.I believe the documents were based on Judeo-Christian principles, but do not call us a Christian nation, per se.
They founded a Federal Republic founded on Christian principles. Moreover, it was the states, not the federal government, that were the important part of the early Republic. The federal government was established as an agent of the states to perform a few functions, and the last thing the states wanted was for the federal government to create a national church like the Church of England. The states already had established churches or other religious settlements and didn’t want the federal government interfering. For example, the Congregational Church was the established church in Massachusetts until 1833.