This is what I would recommend based on my experience with my wife (then fiancée awaiting our case number from NVC)
About 2-3 weeks after your status changed with USCIS saying they sent your petition to the Department of State, make an inquiry to the NVC asking for your case number via the public inquiry website:
https://travel.state.gov/content/travel/en/us-visas/visa-information-resources/ask-nvc.html
When you make the public inquiry with them, there is a button to attach files. Attach the Approval Notice of the I-129F. In that inquiry, in addition to asking for the case number, you should also ask them to update the email addresses for you and your fiancé(e) by saying something like:
I would also like to make sure you have the petitioner and beneficiary emails updated in your system as follows:
Petitioner Name: John Smith
Petitioner email: john.smith@email.com
Beneficiary Name: Jane Jones
Beneficiary: jane.jones@email.com
I have attached the approval notice for my form I-129F for your review.
We did this and after that we got our case number (on the 2nd inquiry) and my wife and I got every email from the NVC and the embassy throughout the whole process.