Tente isto:
SELECT a.*, CASE WHEN totalPayments>1 THEN 'NO' ELSE 'YES' END IsFirstPayment
FROM(
SELECT p.payment_id,
p.user_id,
ROW_NUMBER() OVER (PARTITION BY p.user_id ORDER BY p.payment_date DESC) AS paymentNumber,
SUM(1) OVER (PARTITION BY p.user_id) AS totalPayments
FROM payment p
) a
WHERE paymentNumber = 1