As far as I know there are 5 different competitions this season that Real Madrid is playing, namely La Liga, Champions League, Copa del Rey, Spanish Super and Club World Cup, but I think Carlo Anceloti's priority is not only La Liga and Champions League. Anceloti definitely wants the Treble Winners title to create history for himself at Real Madrid like Pep Guardiola did. Real Madrid has a good and complete squad, they must be able to maximize the best results this season.
Real Madrid have a very strong squad this season. With the inclusion of Mbappe in the squad, it can be said that no other team has as strong and stable a squad as Madrid. Real Madrid also has an experienced coach like Ancelotti. So if Madrid want to win the title in all 5 competitions, they have the ability to win it. However, it will be very difficult. But it is not impossible for Madrid. Because Madrid has both experienced and talented players and experienced coaches.
But the many injuries experienced by Real Madrid players at this time can hinder Real Madrid's journey to achieve the results that Carlo Anceloti expects, the coach must work very hard so that the club performs well with the players they have and in the first match in the UCL Real Madrid will face the Bundesliga club Stuttgart, it seems this is not too difficult because I am sure Stuttgart will not be able to make it difficult for Real Madrid.
You are right that Madrid's main obstacle to a good performance this season is the injury problem. Madrid's players have been plagued by injuries at a rapid pace this season. Several key players in the squad have suffered injuries. This is why Madrid's performance has been somewhat unstable at the start of the season. Ancelotti was probably not prepared at all for such an eventuality. However, once the players return to the squad, Madrid's performance will be strong again.