Your result
Argentina — Marriage
Not eligible
Then there is no Argentine route here, and that is quick to establish.
The marriage route depends on your spouse being an Argentine citizen. Argentina does not offer anything through a spouse's residency, a spouse's ancestry, or a relationship to any other relative — there is no in-law route, no sibling route and nothing through a partner's own pending claim.
One thing genuinely worth checking before you set this aside. If your spouse has an Argentine parent or grandparent, they may have an Argentine claim of their own that nobody in the family has looked at — Argentina passes citizenship to the children of anyone born there, at any age, with no deadline. If your spouse became Argentine that way, this route would open for you afterwards. It is a two-step path with a wait in it, but it starts with a question worth asking.
Otherwise, the two directions that usually pay off: your own ancestry, since descent routes need no relocation and several countries reach back further than people expect, and residence routes if living abroad is something either of you would consider.
Tell us where your own grandparents and great-grandparents were born, and where your spouse's family is from, and we will tell you which of those is worth pursuing.