He has already smashed two other major records in the 2019/20 season as he became Barcelona's youngest ever goalscorer in La Liga before then becoming the youngest goalscorer in Champions League history.
His performances for the Blaugrana were a ray of light in an otherwise dismal campaign in which they failed to win any silverware for the first time in 12 years.
Enrique has asked for patience with reference to Fati's development but praised the player's abnormal self-confidence.
"When we choose the squad we do not look at his age," the Spain boss said after the Ukraine win.
"That does not mean that we do not have to understand that Ansu Fati will play bad games and will make mistakes many times. It is part of his learning, but that self-confidence is not normal.
"Ansu Fati is very happy. He is only 17-years-old and has to mature, but that in his second game with the national team he dares to do all this...
"He brings hard work and humility. He has trained at an impressive pace and I am glad that he goes home with this joy."
Spain have enjoyed a productive Nations League break as they drew with Germany a few days ago before comfortably defeating Ukraine.
The other scorers on Sunday were Ferran Torres and Sergio Ramos (2).