Absolutely correct - no "must be" requirements exist for salvation, besides that God had chosen that person for salvation from before the foundation of the world, and few there be that can understand or accept that - and that's what makes it by grace - the faith was His, not ours, otherwise it would have to be by our works. He alone as Savior did everything required for salvation on our behalf. From/by/through salvation, we are given faith in Him as Savior as a gift, but that faith an accompaniment to salvation, it does not cause it.
[Tit 3:5 KJV] 5 Not by works of righteousness which we have done, but according to his mercy he saved us, by the washing of regeneration, and renewing of the Holy Ghost;