When a government department requires a document from you, that you cannot produce, those officials have two choices: say NO to your request, or find a legitimate way to make a legal exception for you.
Since you want them to make an exception, it is up to you to demonstrate why they should even consider doing so. It can help if you can show them all the steps that you have tried, to obtain what they are asking for.
Let's just say, for example, that the missing birth certificate is of someone who was born in country x, but that since that time country x has been through a complete political change, such that it no longer exists as country x but now is split up into countries y, z and q. Depending on the circumstances of the parent's birth, you could submit correspondence that you have had with the authorities in y, z, and q.
Even if they never replied to you, submitting your side will show that you have tried to do what the Swiss authorities needed of you.
You could approach the representative of the parent's birth (or citizenship) country in Switzerland (or perhaps in neighbouring countries) to ask them if they can obtain the parent's birth certificate for you. Again, if they reply to say that this cannot be done (e.g. because you'd have to return to that country in person, or that no documents can be issued because there is currently a war there, or because the government archives in that country were burnt down, or because you are no longer a citizen there but now of another newly created country), then you submit that information to the Swiss government department.
Try to find a cultural club (or a church or mosque, etc.) or forum of that parent's birth (or citizenship) country, and ask the people there whether they know of a way to obtain documents from back home. Or the names of any other documents that they've obtained from that country (and how they did so), which were then considered by the Swiss to be acceptable or sufficient.
You could also ask the Swiss authorities whether it is possible to register the baby's birth by using the birth certificate of only one parent, plus, perhaps, another document, such as the marriage certificate, or an affidavit by the father (if he's the one without a birth certificate) that he acknowledges being the baby's father, or a medical report from a hospital certifying that it was the mother (if she's the one without a birth certificate) who gave birth, and/or a DNA test.
You could try to register the baby in the respective countries of the parents' births and/or citizenships, independently of trying to register the birth in Switzerland. It's worth at least enquiring whether this could be possible, since each country will have its own set of requirements, and it may be easier to fulfil those of one of your countries, than of Switzerland. Again, document every step, to prove what you have done, to the Swiss authorities.
If you have other children, you could perhaps demonstrate in what way it was possible to register them (even if their circumstances were different).
In the meantime, ask whether it is in any way possible to obtain some sort of provisional registration of the baby's birth, pending the submission of the missing documents. If you find that you absolutely are not permitted to register the baby's birth fully, because you're missing documents, at least such a provisional registration would give the baby basic papers.
In any case obtain as much documentation as you can from the place where the baby was born, and a certificate by the doctor/midwife in attendance, so there is at least some record.
For any document you submit, provide a proper translation into your municipality's official language. Write all your letters, too, in the local official language, not in English or any other language you command.
Finally, be very, very patient, and just keep plugging away at it, trying, trying, trying to obtain the document required of you, and/or to collect suffiently comprehensive information to enable the authorties to make an exeption for you.