If you look at Liverpool's games for the next 3 to 4 weeks, you can see that they have a match every 3 days and will play against very strong teams like Chelsea, Arsenal, Leipzig or Leverkusen. It's going to be a very tough few weeks for the players and now it will really show whether the new coach has what it takes to replace Jürgen Klopp or whether it's too much for him and the team.
The next games would be, RB Leipzig, Arsenal, Brighton ( EFL Cup ), during the premier league competition and then finally Bayern Leverkusen.
I think Arne Slot has indeed had a good start with Liverpool, having nine wins which is more than any Liverpool manager has ever had, I will agree with you because he needs to win trophies so he can cement his place as the manager who replaced Jurgen Klopp for a long time. For the games they'll be playing, I think they'll lose to Arsenal, and Bayern Leverkusen but the other fixtures are clubs they can currently handle. Replacing Mo Salah, Alexander Arnold and getting a new defensive midfielder should be his priority next transfer window.