The Child and Dependent Credit is non-refundable.
That is true.
However it does lower your tax liability.
If your tax liability is lowered by this non-refundable credit, and refundable credits follow, your refund increases.
Example-
You have a $100 tax liability and a $500 Earned Income Credit, your refund would be $400.
Lets say you get a 200 Child and Dependent Care Credit (which is non-refundable so only 100 counts) and your tax liability goes down to zero. Next the 500 EIC kicks in, your refund is increased to $500.
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