I don't think that's the case. You should be able to take a Lebera or Lycamobile SIM and use it immediately, buying additional credit on vouchers from kiosks.

I don't think that's the case. You should be able to take a Lebera or Lycamobile SIM and use it immediately, buying additional credit on vouchers from kiosks. It's years since I did this, but it's the way for visitors and immigrants to get a Danish phone number before they even have a CPR number.