I believe so.  The rebate was always a credit based on the 2020 tax return, even though the IRS was directed to use 2019 information to make advanced payments.  There is nothing in the law that says you must have a SSN at the beginning (or even the end) of 2020 to qualify, only that you must have the SSN when you file your return. 

Found this if anyone is interested:

If you didn’t receive an Economic Impact Payment because you did not have an SSN that is valid for employment before the due date of the 2019 or 2018 return, you may be able to claim the Recovery Rebate Credit if you are issued an SSN valid for employment before the due date of your 2020 return (including extensions) and meet all other eligibility criteria.  If you are married and file a joint return and did not receive an Economic Impact Payment because either you or your spouse did not have an SSN valid for employment issued before the due date of the return that was used to determine eligibility for the Economic Impact Payment, you may be able to claim the2020  Recovery Rebate Credit if at least one of you has or is issued an SSN valid for employment before the due date of your 2020 return (including extensions).  Similarly, you may be able to claim an additional amount in 2020 Recovery Rebate Credit for a child who has or is issued an SSN valid for employment before the due date of your 2020 tax return (including extensions).

Thank you!