I checked, to get a replacement sim my carrier sends out inactive cards that needs to be activated through their web service using the printed number on the card.
If you don't have an account you need to contact customer service, and to get through there they most likely authenticate you based on your SSN and an already active app on your phone (BankID) where you input your personal password.
This has actually created problems when people get their stuff stolen abroad. The ID application is authenticated using your bank and a device using your physical bank card, a generated number from the webpage and your pin and then the generated number is put into the webpage. So if you get both phone and card stolen it's essentially impossible to get into your accounts until you can get a new one posted to you. Especially fun if your bills end up in a digital mailbox requiring that login....
Using that app is how essentially all identification is done in Sweden since it's based on an already approved physical device and a personal password. With your bank as insurance that the information is correct based on your physical bank card and the account associated to it.