You wrote:
“This statement seems to be saying that some people, no matter what they believe, if they wind up saved, it is because of Jesus, even though they never expressed belief in Him. This statement does not seem to be an unequivocal support for His words: “I am the Way, the Truth, and the Life. No man cometh to Father except through me.””
Anyone who ends up in heaven ends up there because of Christ. Deciding who gets there is - thankfully - well above my pay grade. Will children who never knew Christ all be sent to hell? Will all human beings, hundred of billions of them, who never knew Christ, but many millions who sought out God sincerely, be sent to hell? If even one of those kids, or one of those others who never knew Christ is saved, it will be because of Christ. I leave all of that up to Him for He is the Savior.