What government action first allowed American businessmen to come to China in large numbers?

Signing of the Burlingame Treaty

Explanation:

The government action that first allowed American businessmen to come to China in large numbers is the "Signing of the Burlingame Treaty."

This was signed in 1868 in Washington, DC, and ratified in 1869. It specifies an agreeable connection between China and the United States.

The Burlingame Treaty ensures both China and the United States have the right to move freely to either country without restrictions.