Have you already filed a 2019 return ? If not will you ? Are you required to file ?
Or a stimulus return ?
Did you get the first stimulus check yet ?
Was this a child born in 2020?
As Critter already said, you cannot get the child based $500 Stimulus payment, in 2019, for a child born in 2020. But, in essence, the 2019 stimulus money acts as an advance of your 2020 income tax refund. This means when you prepare your 2020 income tax return, whoever claims the child, as a dependent, will get the $500.
So, that brings up the question, who can claim the child, the parent or the grandparent?
A child can be the “qualifying child” dependent of any close relative in the household. If you and the parent live in the same household, you may decide between you who will claim the child. Only if you can't agree, do the IRS rules govern.