Need a complete example of API testing Selenium to fill a form

The requirement is to fill a lengthy form (with radio buttons, drop downs, text boxes, three-dotted buttons). Since UI testing is pretty time consuming, we have decided to move to API testing. Currently, we use Fitnesse, Selenium, Java, Maven and JUnit for the UI testing, but the idea is to remove Fitnesse from the scene, and move to API testing. I need a complete example of something like, new user sign up for gmail, where a form needs to be filled.