I am somewhat confused here. This post is labeled as Jira Service Desk, but you appear to be asking questions on creating a sprint. That is specifically a function that is provided by Jira Agile/Jira Software. You are correct that the Jira Service Desk REST API cannot create a sprint.
You can create a sprint via a REST API call, but you will need to have Jira Software or Jira Agile (in Jira 6.x and older versions) to be able to do this. I would recommend checking out the Jira Server Agile 7.3.1 REST API reference page or conversely the Jira Software Cloud REST API page for more details on how you can do this.
Connect with like-minded Atlassian users at free events near you!Find a group
Connect with like-minded Atlassian users at free events near you!
Unfortunately there are no AUG chapters near you at the moment.Start an AUG
We're bringing product updates and pro tips on teamwork to ten cities around the world.Save your spot