They face opponents in Crotone who are back in Italy's top flight after finishing as runners-up in Serie B last season.
After their inconsistency throughout last season, it took three wins from their remaining five matches for Genoa to retain their top-flight status for a 14th year in succession.
All things considered, it was a near miss for one of Italian's football oldest clubs, but they have been proactive in trying to recover from the wake-up call they were given at a time when finances are just as important as matters on the pitch.
Genoa have recently appointed the experienced Rolando Maran, who has a point to prove after he was dismissed at Cagliari in March due to going 12 matches without a win.
As for Crotone, they are back in Serie A for just the third time in their history after responding positively to their relegation back in 2017-18.
Although they only claimed 12th spot during the following campaign, I Pitagorici won over half their games last year to finish the season in second spot, seven points above third.
Nigerian forward Simeon Nwankwo has emerged as their star performer, netting 34 times over the last two campaigns to secure Crotone's return to the big time.
Giovanni Stroppa has also won the race to sign Chilean prospect Luis Rojas for £2.16m, a significant outlay for a team who will acknowledge that they are one of the favourites for relegation.
Genoa form (pre-season friendlies): WW
Crotone form (pre-season friendlies): W
Genoa are expected to start with a five-man midfield, with the experienced Lasse Schone taking his place in the middle.
Crotone are also having to contend with a ban as Jean Lambert Evans sits out the first match of the season.
Stroppa could line up in a similar style to counterpart Maran, using Junior Messias to partner Nwankwo in attack.
Genoa possible starting lineup:
Perin; Biraschi, Zapata, Goldaniga; Ghiglione, Lerager, Schone, Zajc, Criscito; Destro, Pandev
Crotone possible starting lineup:
Cordaz; Magallan, Marrone, Golemic; Rispoli, Henrique, Cigarini, Zanellato, Molina; Nwankwo, Messias
We say: Genoa 2-1 Crotone
Given their close call last season, it has to be expected that Genoa will be much improved during this campaign. While Crotone may have first-game adrenaline running through their team, we feel that the home side will edge out the newcomers this weekend.