You are better off filing married filing jointly. You can do this with an election from page 8 of Publication 519, Choosing Resident Alien Status. You would both need to declare your worldwide income for calendar year 2019. Your spouse can utilize foreign tax credit to help offset any double taxation on his income earned outside the US.
You would need to print and mail your return and attach the election to file married filing jointly to your return when mailed.
You would need to file an extension until October 15, 2020. Hopefully, you will receive the SSN by then. To file jointly, you would need to receive the SSN by the extended due date of the return.
There is a problem with filing married filing separately to claim an exemption for your spouse. Exemptions for spouse and children are no longer available for for US tax filings. However if you file married filing jointly you can receive a standard deduction of $24,400.
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