I have an original certificate. It is not unreasonable to expect to see one from BO - especially since he refers, in his book, to one in his possesion.
What computer generated certificates are you refering to in the early 60’s??? The only recording back then was microfiche. Are you thinking about present day computer scanned copies of microfiche? Surely!
The certificates were provided in just a few minutes, all nice and neat, and run off by a chain printer on snap apart 20 lb paper.
They were "signed by computer" ~ and yes, there were devices in 1962 called "computers" and they did stuff.
What we didn't have at that time were "chips" ~ they showed up in widespread commercial use a little later. The IBM 360 still used "core" technology in 1969, but that line as it was further developed switched to chips as fast as they could be provided. I think the IBM chip factory in Manassas VA was built by the early 1970s.
Obama was born during an era when the US government had taken the lead in tasking then nascent computer systems with performing large scale administrative tasks, e.g. Social Security, Income Tax, federal personnel system, DOD logistics, ICBM targeting systems, atom bomb tests, etc.
The State of Hawaii had only recently been formed out of the Territory of Hawaii. No doubt they were one of the earliest states to sign on to using computers. Indiana was too.
Civil registration laws, however, were in place for 50+ years at the time and a line in a church baptismal book was no longer sufficient. The governments maintained the files, then the data bases, and they still do that function.