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.
...be more productive while being fun to use at the same time. For some, getting started can be a bit intimidating. This is especially true if Jira Service Desk is your first exposure to Atlassian...
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