Basle also started against Romanian opposition at this stage last season, and fell to a 2-1 defeat to CFR 1907 Cluj after conceding twice in the first 12 minutes, going on to finish third in the group and drop into the Europa League.
But after watching them thrash Servette 4-0 on Saturday in the league, Fink believes his team can do better this time around.
"I was very satisfied with the performance of my team," Fink said. "I was very happy that we kept a clean sheet, which can give us confidence for the next few games.
"If we can have a similar performance to the one against Servette, we will beat Galati."
While Basle had a disappointing experience in the Champions League this time last year, the Galati team have virtually no experience at all.
Only one player in the squad, Sorin Frunza, has previously played any Champions League football, and his resume stretches to just five appearances, two as a substitute, for FC Unirea Urziceni two years ago.
Earlier this summer, club captain Sergiu Costin likened the challenge of a first Champions League campaign to scaling Everest.
But after they won their first ever Romanian league title last season, coach Dorinel Munteanu has told his team to believe they can compete.
"I am not feeling any emotion, and I hope my players leave their emotions at home too," he said.
"Even if this is our first time in the competition, we must believe in ourselves, we must be focused and very determined.
"We go to Basle looking to get a point or points. It is difficult but not impossible.
"We have studied the team from Basle, they have a good team with extensive experience in European competition.
"But we hope to be a pleasant surprise in this group."