If I except the monthly stimulus payments would I have to claim it at the beginning of 2022?

If you are referring the advance Child Tax Credit that will become available each month from July through December 2021, those advance payments must be reconciled on your 2021 tax return that you file next year.

There are no monthly "stimulus payments" but there will be monthly child tax credit payments beginning in July.   If you will not be claiming the child on your 2021 tax return and do not wish to repay the monthly amounts by having to reconcile them on a 2021 return, you can unenroll in the monthly payments.   

https://www.irs.gov/credits-deductions/advance-child-tax-credit-payments-in-2021