If we spread out all the worldwide social welfare resources among all the people worldwide who would require social welfare, the average would be so far below the current levels of first world social welfare that it's basically the same as the system had been destroyed.

It's not about finite vs infinite, it's about the notion that currently "the good social infrastructure" in the first world can cover a small portion of the global population, doesn't have much excess capacity, and is obviously not sufficient to provide a comparable level of life/service/whatever to everyone in the world. Dividing it equally would mean a regression to the global average which is unacceptably low compared to first world standards, so the first world would never accept this.