Was pregnant and gave birth but my child passed the same day. Do I still claim my child? I have birth and death certificate, and also social security

Yes, you can claim the child as your dependent on your 2019 tax return as you do have all the required documentation and their SS number.  When entering them as a dependent make sure that you indicate that they passed away in 2019 and the date of their passing.

Additionally, when entering the child's information you will be asked how long the child lived with you.  You should select the whole year since a child born during the year is considered living with you for the entire year.  Even if the child was born and died during the same year.