Apache kylin cube creation with rest API
Yes, it is possible to create project/model/cube with the rest API, because Kylin web is communicating with backend through the rest API. You can study how it works in Chrom's console.
But I would recommend you to create them from Kylin's web GUI, as there are some logic and validations in the front-end code. The structure of Cube definition is inclined to change in the future version, then you may need to update your client code if not using Kylin's web GUI.