If you already e-filed, don't do the non-filers return. It is considered a simple return, so it will be rejected.
If you claimed him as a dependent on the 2019 return and he was under 17, you did qualify to receive the $500 stimulus. However, the IRS has not given TurboTax any official guidance as to when stimulus payments for every person will be released.
If you don't receive the stimulus payment in 2020, you can always receive it as a credit on your 2020 return in 2021. The stimulus is actually an ADVANCE on a credit on your 2020 return.