You can't claim any dependent unless they are a US person first. This means US citizen or US resident. If your child is not a US citizen you can't claim them regardless of form 8332.
If the child is a US citizen, then you need form 8332. Since the other parent does not have an SSN, I suggest that you ask the other parent to fill out form 8332 with all the other information, sign it, and then express it to you in the US so you have the original with an original signature on it, not a copy. Also ask your ex to provide a photo copy of the first page of their foreign passport. You would mail the IRS the form 8332, the copy of their passport, and a brief letter explaining that the other parent does not have an SSN and that you are claiming the dependent because you have a release and you have paid the child expenses.
