Cutting a babies hair before the baby turns 1 year old won't change the texture of the babies hair but it will give the baby a bad hair do if you cut the hair of the baby before 1 year of age.
It's best to wait until after the babies first birthday before you give them a hair cut otherwise it could mess up their hair.
Hair texture won't change though unless chemo is needed and hair texture is also determined by genetics.
For example your baby might have curly hair when born but when they hit puberty the babies hair could change from curly to straight but that has nothing to do with cutting the babies hair but is also determined by genetics.