If my child's father pays for the daycare expenses through his FSA and I claim them, can I claim the child/dependent care credit even though it wasn't paid by me?

We are an unmarried a couple and shared 2 biological children. Can we max out his FSA and claim the child/dependent care for both children? Or it is better to just claim the tax credit for both children? He makes over $50k, while I make $30k. Which route should we take? Our daycare fees are around $8,000.