Breast fed baby will NOT take bottle. But...

So get this!!! My 4 month old baby girl WILL NOT take a bottle no matter what brand or type of nipple. I’ve tried so many, avent, comotomo, nuk and many others. She’s been eyeing out food and has been eager to start solids. So with complete approval from our doctor we started her ok purée foods. Still keeping the normal nursing schedule....BUT for some reason today I felt a little adventurous and put an empty NUK sippy cup with sippy nipple to her mouth. So SUCKED ON IT, I than put a tiny amount of breast milk in it and she took it. I was stunned. but when I looked it up, the brand states that the bottle/ sippy cup is for 6- 18 month olds. (I’m planning on asking our doctor.) but does this make sense? Does anyone have a 4 month old starting with sippy cup right after breastfeeding? I’m so confused....she going to a baby sitter in soon because I’m starting work shortly. Am I’m really going to send my 4 month old daughter to a babysitter with a sippy cup and not a bottle??