since your not in contact with each other, it would seem neither could file joint. by law, both spouses must consent to a joint return. so you're left with married filing separate. you'll have to paper file and include a statement that you couldn't obtain spouse's SSN. provide her name and last known address.
if you lived apart from your spouse for the last six months of 2019 and paid more than 1/2 the cost of keeping up a home for yourself and your child who you could claim as a dependent and who lived with you for more than six months in 2019 you could file as head of household and then not need spouse's ssn.