Puss was a Soldier, a made guy who had served in Tony's crew and had also served as a Soldier under Tony's father Johnny Boy.

Pussy would've been promotded to Capo/Underboss in Season 2 if Tony's subconscious didn't "know" that Puss was a rat. All throughout Season 2, Tony, deep down, knows Pussy's a rat, but doesn't want to confront it and the outcome of finding it out, so he buried it...until that fever dream. As such Paulie got the promotion instead. Had there been no suspicion, Pussy would've made Underboss or Consigliere.

At the time of the beginning of the series, Junior, Ray Curto, Paulie and Pussy were the guys who went back in the family the longest. All had been associates or made guys since the '60s. All the other guys didn't come up till later on, in the '70s and '80s.