Children have limited ability to process the right and wrong of their own actions. This is especially true for infants but still relevant for older children. It's difficult to say at what age a child becomes old enough (or experienced enough) to understand the lessons behind the mark and therefore be capable of making the kind of decision which the Mark is aimed at forcing people to make; God or money.
But God is able. He can look at the heart of each individual and make his own judgment on the motivations behind why people take the Mark. An infant or toddler will not understand the concept of worry about material needs; they simply assume that their needs will be met which is probably at least part of the reason why Jesus talked about becoming like little children (i.e. trusting that God will meet our needs). It will be similar to people with a mental challenge; if they are not able to understand the issues God will know and judge according to what he thinks is fair in the context.
I'm guessing you are asking how there can be people who survive if they reject their only means of buying/selling (i.e. the Mark). Jesus addressed this issue, too, by promising that God will take care of anyone who steps out in faith and seeks his kingdom first. There is no specific blueprint or rule book to list exactly how God will provide in every circumstance, but it still works.
Consider the early disciples. Jesus wanted them to understand this same lesson so he sent them out into the world, commanding them not to take any food, money or extra clothing (Luke 10:4). Later, he asked them if they lacked anything when he sent them out into the world with nothing and they said, "no" (Luke 22:35). He told them, "the laborer is worthy of his hire". God is our employer now and we are the laborers. The creator of the universe will take care of us if we work for him.
He said the whole world runs after what they will eat, drink, and wear, but that we should not be like them. He asked us to consider the birds and flowers specifically because they do not work for money, and yet God still feeds and clothes them. He said that we have a choice between working for two masters; one master is God and the other master is mammon (money and the things money can buy). He said we will love one and despise the other (Matthew 6:24-34).
We show our contempt for God's kingdom of love/sharing when we demand payment for our help. In the same way, we show our contempt for the monetary system when we refuse to force payment.