Create a table with a json column:

  CREATE TABLE Doc (
    id UUID PRIMARY KEY,
    val JSONB NOT NULL
  );

  ALTER TABLE Doc ADD CONSTRAINT check_doc_val CHECK (
    jsonb_typeof(val)='object' AND
    val ? 'user_id' AND
    jsonb_typeof(val->'user_id')='string'
  );
  CREATE INDEX doc_user_id ON Doc ((val->>'user_id'));

I am also a little worried about performance (maybe prematurely). If that document is large, you will be rewriting the entire json blob each time you modify anything in it. A properly normalized schema can get away with a lot less rewriting?