Random sampling performance

I have an ElasticSearch index with 20+ million documents, which I'm using
to perform GeoBoundingBox filters, combined to other queries.
I'd like to have, for each search, a random sample from my results.
After reading the documentation, I tried using the RandomScoreFunction,
which gives a random score to each result from my queries.
The problem is performance wise. Applying this over around 10 million
documents (which can happen sometimes), takes more than
10 seconds. Actually there the ES cluster have 6 servers, and 10 seconds is
quite a long time for the kind of application I want.
Is there anyway to get a consistent sample from my results, preferably
having a good geographical distribution?

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