In order to receive the full $2000 child tax credit for 2020, as well as earned income credit if you are eligible, you must submit an on-time tax return that contains the Social Security number. An on-time tax return is one that is filed by October 15, if you received the extension, which you said you did. For 2020 only, claiming a dependent with Social Security number will also get you the $1100 recovery rebate which represents the round 1 and round two of the economic stimulus. (And the child must be age 16 or less as of December 31, 2020.)
If you file before receiving the SSN, you can’t list your child as a dependent. If you file an amended return after receiving the SSN, you could receive the $500 credit for “other dependent” but you would not receive the full child tax credit or EIC or recovery rebate. Or if you file an original return with the SSN but after October 15, you would receive the $500 other dependent credit but not the other credits and rebates.
