In "In The Godfather Garden" it says:
"According to conversations taped by the FBI between Tony Boy, Gyp DeCarlo and Sam "The Plumber" DeCavalcante, the Boot was initiated as a caporegime, or captain, in the Luciano crime family in 1946, around the same time his colleague in crime Jerry Catena also became a "made" man."

So if I'm interpreting that correctly, the Boot became made and automatically became a captain. Interesting. Also interesting that he and Catena were both made so late.

https://www.maryferrell.org/showDoc.html?docId=141729&relPageId=6&search=funzi
And according to this conversation between DeCarlo and Little Pussy Russo, Funzi Tieri was indeed under Mike Miranda until Genovese made him a captain.