The baby diapers run out very fast. The big case (no matter what sizes, from size 1 to 4 sold in Costco) can only last one month or less. Although the smaller the size, the more diapers in that case, the yonger the baby, the more frequently the diaper has to be changed. Young baby skin is very sensitive, 3 - 5 min after pupu without changing diaper could result in diaper rash.
So for the gift, I would suggest buy another baby-must-have item, that is the diaper rash ointment. The best brand name I have found is Desitin. It magically makes the worst diaper rash disappear over night (maybe an exaggration, but it works amazingly well on diaper rash). Try to see if you can find this in Costco. It can be found in the baby item shelf of most supermarket or drug store
If you really want to be go-into-detail, buy a box of cotton swap (don't buy it in Costco, for the package there is too big) for applying the desitin on the little EGG's tender buttom.