I also initially thought the same as you, Milan will give their best performance this season with their new coach, but it turns out that Milan's performance was very disappointing at the beginning of this season and has not been able to get full points, while their rivals such as Inter and Juventus have won more points in the last 3 matches and are in first and second place in the standings, while Milan is in 14th place for the time being.
Milan will most likely have difficulty competing in the UCL because their first opponent is a top EPL club, while Liverpool, while in their best form, I think Milan will have difficulty facing Liverpool.
Against all odds we are having few teams at their worst in Italian league specially AS Roma and AC Milan are having terrible time even we are had some good attacking soccer from the AC Milan, but their defense is not perfect as they needed they are conceding two goals in every game mean things are surely looking for improvement.
No doubt if they will be play like this we will have no good time for them in UEFA Champions League, and they will be faced early exit which will be not good deal for them because they are having second-best record in this competition. They are going to face big teams specially Liverpool which is famous for their aggressive approach and their start in Premier League is impressive, so things can go against them badly if they are not going to have some good changes for improving their defense we have short time and challenges are big.