Usually used for long running queries but sometimes appropriate for this problem is creating a "query" resource via POST after which you have a URI for the results:

  POST /queries
  
  {"query": "..."}
  
  201 Created
  Location: /queries/1001
  

GET the results:

  GET /queries/1001
  
  {"results": ...}

You could optionally return results in the POST response too but I'm unsure whether that strictly conforms to the HTTP spec or not.