Every baby is different my dear! I've had three in cloth bums and though I've used motherease as our basic nappy with all of them, their different shapes and sizes meant we have had a journey through lots of different makes/sizes along the way! My third in particular seemed to out-pee his size 1 little lambs/totsbots very early, the girls were OK with them til much later. My middle child was chubby and outgrew her motherease onesize at the waist for several months til she slImmed through toddling, we needed size 3 totsbots and Toddle-Eases for a while.
So yes, it's normal for babies not to fit the "standard" size. Just try lots of different things til you get a good make/style/size.