Under manager Gareth Southgate, England have come close to ending a 58-year drought to win a major tournament on three occasions without getting over the line.
Kane won the Golden Boot as Southgate's men bowed out to Croatia at the semi-finals of the 2018 World Cup and then missed a crucial late penalty in a quarter-final exit to France four years later.
But it was on home soil at the last European Championship that England came closest to glory under Southgate as they lost the final on penalties to Italy at Wembley.
Since then, the development of Jude Bellingham, Phil Foden and Bukayo Saka has helped form a fearsome attacking arsenal alongside Bayern Munich striker Kane.
Between them the quartet scored 114 goals for their club sides this season.
"Every tournament poses different expectations but we've earned the right to be classed as one of the favourites," Kane told a pre-match press conference in Gelsenkirchen.
"We're here to win ultimately and there will be nothing better than to do that for the nation.
"There's a lot of top teams and tomorrow night is our focus. We know how tough it was to get to the final last time.
"We're going to have to do that again and even more if we want to do that again and hopefully one step further."
Southgate, though, warned his side will have to be "exceptional" to beat Europe's best.
Germany crushed Scotland 5-1 to open the tournament in style on Friday, while Spain swept aside Croatia 3-0 on Saturday with three first-half goals.
England are expected to cruise through a group also containing Denmark and Slovenia.
But Southgate has stressed the importance of taking one step at a time on what he has speculated could well be his final tournament in charge.
"You've seen Germany play the way they did last night, Spain in the first half today. There are a lot of good teams in this tournament. We have to be exceptional to progress through the group and have the opportunity to go further," said Southgate.
"Our focus is to qualify from the group. When you're trying to achieve exceptional things you have to break it down into chunks. Our first priority is to get through the group and work from there."
A heartbreaking defeat to Italy in the final three years ago compounded a damaging night for English football.
Thousands of ticketless fans stormed the turnstiles and disabled entrances of Wembley in ugly scenes that marred the final.
German police have labelled Sunday's fixture "high risk", with only reduced-strength beer available to fans at Schalke's home stadium.
Southgate called on the tens of thousands that will travel from England for the match to enjoy themselves responsibly.
"I expect everyone to enjoy the football," he added.
"I've been fortunate to travel to a lot of football tournaments and they're great carnivals and great chances to meet people from different parts of the world.
"The whole of Europe can come together and support their team and get behind their team."
