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I know it is an old question, but now it is possible to use random_score,
with the following search query:

{
   "size": 1,
   "query": {
      "function_score": {
         "functions": [
            {
               "random_score": {
                  "seed": "1477072619038"
               }
            }
         ]
      }
   }
}

For me it is very fast with about 2 million documents.

I use current timestamp as seed, but you can use anything you like. The best is if you use the same seed, you will get the same results. So you can use your user’s session id as seed and all users will have different order.

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