I have tried this API and 200 returned.
https://circleci.com/docs/api/#trigger-a-new-build-by-project-preview
Although the jobs were created, the job statuses were ‘Not Run’ while “Only build pull requests” option in advanced settings was on.
Then, I turned off “Only build pull requests” option, and the job began to work.
This option must be turned off to use this API ?