There are a few issues with doing research at present for Scottish certs and registrations...
Scotlands People as Carol has mentioned is where you need to check details. Free to register and run searches. You only pay to view images online, or when ordering a certificate. At the moment you cannot order any certificates as their offices remain closed for this type of business due to Covid. There is a 100 yr cut off to view birth certs online (75 yrs for marriages and 50 yrs for deaths) to protect people's privacy etc.
Unlike English and Welsh records, you can't search for births online using mother's maiden name. On the index therefore you will only be able to see a surname with no further details. You can't take from that the surname is that of a child with married parents or the mother's maiden name. Sometimes if father agrees to have his name included in a child's birth registration, there will be two entries on the register index, one for the father's surname and one for the mother's surname.
If you were able to search in Scotland in person when the major genealogy centres open, you can do a search using mother's maiden name from c. 1929 which would fit with your years. If this search is being done in person, you can also view the image online at their terminals to check the details for the registration...but for now, these remain closed.
Monica