The Primera Division new boys have won three and drawn one of their opening four games to sit joint third in the table.
Real Madrid are the only side to have taken points from the Yellow Submarine so far.
Giovani has played his part, with three goals in four games since joining from Real Mallorca in the summer, including the equaliser in the 2-2 draw at home to Madrid in their last game.
"I came here with the idea of helping the team and I'm doing it," the Mexican told a press conference. "I'm happy and calm. Without doubt, I have never felt so good both physically and personally.
"I think it has been the best start since I became a professional. But it is important to be cautious. You always need to be cautious at the beginning of the season."
Giovani is only 24, but is already at his seventh club. He believes, though, he has settled in easily this time.
"I've noticed that this club is like a family, there is a good atmosphere among the players," he said.
"The team is doing well and that means each day there is a better atmosphere in the dressing room."
On Sunday the visitors travel to face a Celta side who suffered their first loss of the season, 3-2 at Athletic Bilbao, last time out.
The hosts are sweating on the fitness of Danish midfielder Michael Krohn-Dehli, who is a doubt because of an injury to his right adductor.