Kane joined the perennial Bundesliga champions from Tottenham in a deal worth at least £100million in July after nine years at his boyhood club without winning a trophy.
The England captain, who is preparing for Saturday's Euros qualifier against Ukraine in Wroclaw, Poland, has already scored three times in as many starts for his new club and believes playing in a more pressured environment will make him a better player by Euro 2024, which will be held in Germany.
"I believe it will," Kane said. "Whether I win or not, the decision [to join Bayern] came down to putting me in those situations.
"With Bayern Munich sometimes we expect them to win because they have won [the Bundesliga title] for the last 11 or 12 years or whatever it has been.
"But in my short period there is still a lot of pressure to win these trophies. We have not won the cup for a few years and we have not won the Champions League for a few years, so there is definitely a lot to gain and a lot of pressure to take.
"Time will tell, but at the moment I am enjoying that feeling.
"It’s definitely a different pressure compared to what I felt at Spurs. Of course we wanted to win things at Spurs but if you went a couple of games without winning then it wasn’t a disaster.
"The feeling at Bayern is that you have to win every game. We won the first two games 4-0 and 3-1 and there was still talk about not being too happy about the way we played. That’s part and parcel of being at one of the biggest clubs in the world.
"Of course, there is no hiding the fact it [silverware] is the one thing missing from my career at the moment and when you have got players in the [England] squad who have won things you want to be part of that as well and have those experiences as well," Kane added.
"Just the experiences of having title runs and cup runs and hopefully a Champions League run will only add, hopefully, to handling pressure in certain situations. If we are going to win anything with England we are going to have to deal with that.
"Me, being captain, I want to put myself in that position as much as possible."
Over the years, Kane has watched several of his England teammates win the biggest prizes in the game, among them Kyle Walker, who left Spurs for Manchester City in 2017 and has won 13 major honours, including five League titles and the Champions League.
The 30-year-old admitted it occasionally "hurt" seeing his colleagues winning silverware and said it motivated him to claim his first club trophies with Bayern.
"As a competitor, when the boys are playing the Champions League and I am just sitting at home watching it, I would be lying if I said there wasn’t a part of me that hurt," he said.
"Of course, I want them to do well -- Kyle and all those guys to win when they are in competitions I am not in -- but a part of me wants to have those experiences. With the other players in the team having done that, I am not sure jealous is the right word, but it does motivate me to go on and try to push myself towards some of those trophies the guys have got."
There was long a suggestion that Kane was reluctant to leave English football while he remained in the hunt for the all-time Premier League scoring record but he left Spurs just 47 goals shy of Alan Shearer's total of 260.
"I think there was a lot of talk about it and the fact I was getting closer to it but I have never been anybody who has chased individual honours ahead of team awards," Kane said.
"Ultimately it comes down to me to see how good I can be and I felt like I had to be playing Champions League football and competing for titles each year. Bayern Munich definitely gives me that.
"The record of course would be amazing and it might be amazing if one day I do end up breaking it. But it is not why I play football and my move shows that."
This year's Champions League Final will be held at Wembley, while the European Championship will be held in Kane's new home, Germany, with Kane conscious it would be a script writer's dream if he could do the double with Bayern and England.
"I have been told about the Champions League final in Wembley, for sure, and I know the Euros are in Germany next summer so if there’s someone out there writing a movie, I will try and do my best to make it happen!" Kane said.
"It’s hard. There’s so much time to go I don’t want to think about it too much, but if it did happen it would be incredible."