Babies who are born in the UK but do not have a claim on British citizenship get a special status called "tolerated". It means they do not necessarily need a British visa because the government recognises that there are circumstantial practicalities surrounding newborn babies where immigration rules are concerned.
If the child stays in the UK (without leaving, and strenuous proof is required) until they reach the age of 10, they can obtain British citizenship, but few children go this route for obvious reasons.
More commonly the child leaves the UK with their parents and subsequently returns. Once the baby leaves the UK their "tolerated" status is permanently revoked and they become "undocumented". This changes the situation because the child will arrive at a border control and that kicks off at least three procedures...
And they can be right-up-in-your-face aggressive about these things. In theory the question of documentation is not an issue at the border because the government requires carriers to prevent the arrival of undocumented passengers (or they get fined when they are in breach).
Because of these things the government expects the parents to sort out reentry issues before they leave or to sort things out before they return.
In your case the child has an EU passport in the pipeline, but it may not be ready by the time you travel. And so the child will travel on a non-EU passport. It means you need to take the non-EU passport and get a family permit (or other sticker) for it before you return to the UK. You may be able to pursue an inland option before leaving and to explore this possibility any Citizens Advice Bureau with Level 3 Competence (see the Immigration and Asylum Act 1999, Sections 84 and 85) will provide you with a brochure and reliable advice for free (it's important to verify their competence level before making an appointment, you need Level 3 or higher).
If at least one of the parents has a settled status in the UK (i.e., either permanent residence or indefinite leave to remain) then the child is already British and you can use the Passport Office to obtain a British passport. But since the applicant is a newborn, extra rules kick in and it will probably take longer than getting the EU passport (newborns cannot use the express service).