" A computer capable of deriving the correct settings.." "..much variable data in realtime "
In fact each of the engines had 13 "computers" or controllers to do the analysis, covering inlets, outlets, after burners etc.
This is the 60's. "Computer" does not have to be digital. AFAIK most of them were analogue. Operational amplifiers and sets of resistors.
But calibrating them....
However you're right the design pushed the SOA a long way. Duncan Sandys had done a first class job of kneecapping the UK military aircraft industry in 1957 so they had limited experience of >M1 flight. It was said at the time Concorde was as challenging to Britain and France as Apollo was to the US, but in reality it was more like the Shuttle.
BTW the French wanted it to be even smaller and shorter range. It took IIRC 2 re-designs before the French grudgingly accepted it had to be at least 100 passengers. Ideally it should have been able to fly from Frankfurt, the other big European transport hub for the US (and that would have given the Schipol as well).