Someone from outside the organization
While I'd bet that the Cardinals would use one of the aforementioned options, there's always the possibility that they could sign or trade for a new first baseman next offseason.
I know I left out Luken Baker, but I just don't think the Cardinals are envisioning a world where he takes over first base for them. Thomas Saggese is a name that has been thrown around and I could see happening, but I think they'd rather use him as a utility infielder than stick him at first base. That's also a lot of pressure to put on his bat to perform if that's his new position.
I also do not see the Cardinals moving Jordan Walker to first base. They've repeatedly shot down the idea and believe he has what it takes to become at least an average outfielder defensively. It's also not just a given that he can play first base well. It's not a natural position for him either, and while the transition to first base works well for some players, plenty of players have proven it's not an easy position to play.
Next offseason, Pete Alonso headlines a strong class of first baseman, as he will be joined by the likes of Goldschmidt and Christian Walker, while the likes of Cody Bellinger, Rhys Hoskins, and Anthony Rizzo could opt out of their contracts as well. The obvious play would be a reunion with Goldschmidt, but if that is not working out, any of those names could come into St. Louis and replace Goldschmidt in the lineup.
The following offseason, names like Vlad Guerrero Jr., Josh Naylor, Ty France, Luis Arraez, Kyle Schwarber, and Joc Pederson all hit the market, so any one of those guys could be available in a trade next offseason if their club is looking to recoup value before losing them.
While this is the least likely of options for St. Louis, it's still possible, and let's be honest, it's only February. A lot can and will happen between now and next offseason, so who knows where the Cardinals will be by then? It still feels like Goldschmidt will finish his career as a Cardinal, but we'll have to see how things play out as the season goes on.