The REST API is not a data source that Tableau Desktop can access. You must export the data from an API request to a csv or other flat file in order to use the REST API. After that, you may use Tableau Desktop to connect to that file. Python may be used to automate this process. You may also directly export from Postman. After you've ran your GET, go to the top of your results and download the file.
However, I strongly advise you to implement this in Python rather than Postman so that you can use pandas to consume the json file much more quickly. Instead of utilising the API directly, I would prefer using tableauserverclient in Python. The tableauserverclient is more restrictive than the API, but it will almost certainly provide you with the capabilities you want.