If my spouse no longer lives in US and never had a social security number, how do I choose a filing status if I'm legally married but we're separated (non-legally)?

That is discussed here:

https://ttlc.intuit.com/community/retirement/discussion/how-do-i-file-separate-without-spouses-social-security-number/00/758805/amp

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@campbellsere wrote:
I haven't spoken with my spouse in years but have been unable to file for divorce. He no longer lives in the US and left the country before becoming a citizen. If I file as married filing separately, it still asks for his social security number, which he never had.

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If you have a child, step child or foster child you can probably file Head of Household.

Otherwise your only choice is Married Separate and print and mail the return and write NRA (non resident alien) in place of the SSN.

We cannot give legal advice, but you should probably see an attorney.   Abandonment can be grounds for divorce without the spouse being present.