Meatballs show up in cuisines all over the world, from the most ancient written recipes to today. There's no reason to think they had a single origin. They're just too ubiquitous. I mean, form minced meat into a clump and you have a meatball.

The big question is probably what role the Persian kofta had in popularizing meatballs worldwide. However, considering that Muslim culture never penetrated to quite a few parts of the world which have meatballs in their cuisines (Scandinavia and The Philippines come to mind), I doubt the kofta is the ur-meatball.

And, yes, Sweden and Denmark have indigenous meatball traditions going back at least back to the mid 19th century.