Make a hat and blanket. A baby never outgrows a blanket and hats and socks are fine for 0-3 month sizes. Otherwise make a 2T sweater. Something for the baby to grow into.
My newest Grandson (8 weeks old this Thursday) waa 4kg at birth and 3 weeks early, he now is almost 7kg and grown out of newborn sizes ...it's lucky most people bought the next size for him and some of his little suits he never got to wear or only once or twice...my Dil has them bagged up to give to another family member when they are needed
Most newborns don't stay in 0 to 3 months sizes very long, if at all. Many babies are 8 pounds or more today and often start in 6 months sizes.
I would knit something that does not need a size like a blanket or cover that can be used over a carrier for when they have to take baby outside or in a vehicle.
There are some beautiful patterns on Pinterest.