So far he has fulfilled his dream of playing for his favorite club as a child and not long after he was at Madrid, Mbappe has won a trophy which will clearly be very difficult for him to get if he continues with PSG
He has not only chance to play for a club he loves but also has opportunity to lift UEFA Super Cup which was impossible for him to lift with PSG and many years with that club. It's good official start for Mbappe in Real Madrid, a goal and a trophy and onward he will move with bigger targets in this season.
If you look at Mbappe goals and ambitions so far, of course the trophy champions league was his main goal in moving to Madrid, because if he wanted popularity, wealth and domestic trophies would definitely he get all of that at PSG but instead he was willing to cut his salary just to join Madrid at this time, despite all the existing reasons of course Mbappe is already at the best club in the world and we just need to count and see how big his achievements with Madrid will be.
Mbappe is an ambitious player and he will aim at multiple titles in this season including La Liga and Champions League and if possible Coppa del Rey as well but the last trophy is not his main concern. La Liga is a great title but Mbappe will pay most of his focus on Champions League that was out of his reachable hands recent years with PSG.