How can I make the case that limiting advertisers' freedom of expression is justified in the case of banning advertisments to children under 13?
The way to make this case is to say that there has to be a balance between the advertisers' freedom of expression and the needs of society as a whole. You can then say that society has a very strong interest in protecting children under 13 from being excessively influenced by advertisements.
In the US, we acknowledge that not all forms of advertising should be protected by freedom of expression. We ban cigarette advertising on television. We also ban the advertising of hard liquor. We do this because we believe that these ads harm society. If we can do this, we can also ban ads that are aimed at children. We can do so (you can argue) because we need to keep them from being manipulated by advertisers while they are too young to understand what is being done to them.