Before the season manager Thomas Tuchel spoke about needing to "find the right key to open the lock."
Bayern's home opener against Bavarian rivals Augsburg this weekend will provide fans with a chance to judge if their €100 million (£86 million) striker is ready to drive the team forward.
Kane said this week that, off the field, driving has not so far been a problem as he adapts to the right side of the road.
"So far, I haven't had any crashes," Kane said with a laugh.
Kane returned from London on Wednesday after the birth of his fourth child.
At an event organised by one of Bayern's major sponsors, a car company, Kane chose a family-friendly people mover, rather than the usual sports car favoured by millionaire players.
"With four children now, I have to make sure I have enough space," Kane said, telling AFP subsidiary SID "four kids will keep you on your toes."
So will Sunday's opponents, Augsburg, who have won two of their past four league matches against Bayern.
Despite the 4-0 win at Werder Bremen in the season opener, Tuchel said the team needed more consistency.
"We need to reduce the ups and downs, both in the game and between games," Tuchel explained. "We need to improve our stability in a positive way."
Kane's predecessor in the striking role at Bayern, Robert Lewandowski, backed the England captain to deliver in Germany.
"He is a super-striker, he's class," the Barcelona forward said at an awards show in Hamburg, adding that Bayern had pulled off "a great transfer."
Augsburg's 1-0 victory over Bayern in September 2022 set in motion a series of events which would claim the scalp of coach Julian Nagelsmann just a few months later.
After the highs of Kane's debut, Sunday's match will be the next test to see whether Bayern have actually turned the corner.
One to watch: Karim Adeyemi (Borussia Dortmund)
Forward Karim Adeyemi drove Borussia Dortmund to within inches of the title last season, hitting form as the club lost just one of their final 17 league matches.
Adeyemi, who made the move to Dortmund from Salzburg in the summer of 2022, failed to score in his first 13 matches but hit form after Christmas, with six goals and four assists in his final 11 league games.
Manager Edin Terzic called on the Munich-born winger, who is now 21, to deliver more regularly.
"Karim has huge potential, which we see again and again everyday here in Brackel (Dortmund's training ground).
"But there needs to be more consistency and effectiveness.
"That's what we need to bring into his game - and we remind him about that every day at training."
Key stats
60: Exactly 60 years ago on Thursday, the Bundesliga, the first unified nationwide league in what was then West Germany, kicked off for the first time. Of the 60 titles contested so far, Bayern have won 32.
5: Five teams from 1963-64 are in the Bundesliga this season: Werder Bremen, Borussia Dortmund, Eintracht Frankfurt, Stuttgart and inaugural winners Cologne. Bayern were not promoted until two seasons later.
128: Dortmund have gone 128 games without a 0-0 draw, equalling the record held by arch rivals Schalke.
