Would something like this meet your needs?
-- [params]
-- date :start_date
-- date :end_date
SELECT u.id AS user_id, p.id AS post_id, p.created_at
FROM users u
JOIN user_stats us
ON u.id = us.user_id
JOIN posts p
ON u.id = p.user_id
WHERE p.created_at = us.first_post_created_at
AND us.first_post_created_at BETWEEN :start_date::date AND :end_date::date