The best would be to have a public registered address in the CPR register. Thats always enough prove.
If you can not have that in time when moving in to the address, then a signed tenant agreement/ A landlord's statement that you have rented a property from a given date will normally be enough to prove your address, but the A-kasse will make an assessment in every case, so if they are in doubt about if you really live on the address, the A-kasse can demand further prof from you.
But it is off course no problem to live with friends, as long as the address may be considered to be your actual residence. The address must also be considered as your current and usual place of residence.