It did not take long for the Brazilian star to appreciate the playing riches on show on the pitch.
Barcelona chief coach Ernesto Valverde made a decision to rest central defender Gerard Pique at halftime and took Messi off just before the hour mark to give young winger Ousmane Dembele further gametime following his injury.
Alba set up both of Messi's goals in two first-half minutes before the Argentine returned the favour, creating the third goal for the left-back with a wonderful through ball. Lionel Messi was at his best again on Thursday as Barcelona put in a superb display versus Celta Vigo.
"It's a luxury to have him in the team", Alba told Gol Television.
Barca eventually claimed a fifth on the night to compound the visitors' misery, Ousmane Dembele lifting a corner into the box for Ivan Rakitic to bury home with a free header into the top corner of the net from 10 yards out. "We always look for each other to score goals and today we have done it twice", Alba said.
Alvaro Garcia got second-division Cadiz's consolation goal in the 86th, leading to jeers from Sevilla's home fans for the team's shaky finish to the match.
The 53-year-old was seen putting his players through their paces ahead of the return leg of their round of 16 tie at Camp Nou on Thursday, and the presence of and suggested he would be fielding his strongest side.
In a much-changed side, Lucas Vazquez scored both of Real's goals after the 11th and 59th minutes.
Moroccan worldwide Nabil El Zhar scored the crucial away goal for mid-table Leganes on the half-hour mark.