No, the FSA funds are reported in Box 10 of your W-2, when you go to report those funds it is going to credit the amount of Box 10 to your child care expenses for 2021 and then any remaining balance can be elected to be carried forward to 2022. You cannot elect to carry the full amount over to 2022 and then take a child care credit for 2021.
If you show $10,500 on your W-2 in Box 10 and you have child care expenses for 2021. Then you are going to have to report those on your 2021 return. I would request a refund from your FSA for your 2021 child care expenses. Since you are only going to be able to carry forward the excess of your FSA amount in Box 10 and your actual child care expenses for 2021.
