I got some 0-2 month ones from H and M. My son wore it from birth.
Tommee Tippee do 0-3 month sleeping bags that are suitable over 7 pounds I’m sure
I used Love to Dream ones at first, they have sizes starting from 5lbs. Once my baby reached the minimum size for regular sleeping bags we moved on to those (minimum weight varies between brands but usually about 8lb and up).
They normally have a weight on them. It's to make sure they don't sleep through the head hole.