Here are few articles from on here to show him hun.

https://www.bellybelly.com.au/baby/c...sleep-training

https://www.bellybelly.com.au/baby/t...trolled-crying

https://www.bellybelly.com.au/baby/c...art-of-bonding

Hopefully they will help. It's a tough one when both of you disagree hun but if you arm yourself with some research as opposed to just opinion he might be swayed? Also - you are going to be her primary carer and I know that early on I would just do what I felt right - things that DH disagreed with at times but I figured that I was there 24 hours a day and in some things I did know best. I know that sounds awful but it's true. Also - Mia is only 4 weeks old hun, she needs to know you are there to comfort her and to bond with her and even if you decide to go down the CC path - they do not recommend any form of CC until babies are 6 mths old - so you can suggest that to him. Good luck, you are doing an amazing and fantastic job and she is just adorable!!