First Outfit: Size Newborn or 0-3?

Jess
Hi everyone! 
FTM here! I bought for my baby the 2 first "hospital bag outfits" in size 0-3. Then my mom says "ain't those too big? There is a newborn size and it's different as 0-3!!!" I'm kinda clueless now 😂😂😂. Help please?