Mbappe, Neymar and Edinson Cavani starred as PSG laid down a marker with a 3-0 win over the reigning Bundesliga champions in Paris on Wednesday.
Cavani and €222 million arrival Neymar were on target after Dani Alves opened the scoring inside two minutes but 18-year-old Mbappe stole the show with his dazzling display against the Germans.
Mbappe — on an initial loan deal from French champions Monaco — teed up Cavani just past the half-hour mark before terrorising David Alaba as Neymar netted PSG's third in the second half.
"The story is only just beginning," Mbappe told Canal+.
"We knew in our hearts that we had to put in a great performance against a great team. We did that.
"Expectations were high, which is normal after a summer transfer window like ours. It was a complete performance and now we move on to the next match on Saturday. We are here to win every game."
PSG star Marco Verratti was impressed with his team-mate's performance, adding: "Kylian is an exceptional player. He is 18 years old. Being decisive at 18 years like this, it does not happen to many players.
"We try to help as much as possible. Outside the field, he is very humble, he wants to improve a lot. We are really happy for him because these are matches that give him confidence. He is a very important player we are lucky to have here in Paris."
As for captain Thiago Silva, he told Canal+: "Are we stronger this year? Each year, we progress a bit. With Kylian and Neymar's arrivals, we have gone up another notch. The other teams will respect us a little more. Now, we must keep on working."