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Why not just take the Concorde specs and work from there?

Going supersonic, while not trivial, is a well-established technology. Going supersonic economically enough for either airliner or even bizjet travel is another matter. Concorde never even came close.

The only jet which can cruise with a significant supersonic speed (approximately M1.5) without using afterburners is the F-22, and the real magic there is not in the airframe - though it was designed very carefully. The real magic there is in the engine which can provide a lot of thrust at M1.5 even without afterburner. If these guys can develop an engine of whatever size they will need on the full-scale airliner, with the amazing performance of the F-22's engine, then they have a chance that Concorde, with those old-design engines never had.

After that, it's possible the airframe will turn out to look sort of like Concorde (as the Russian TU-144 did). However, the second big issue is sonic boom, which was the excuse given for not allowing Concorde to fly supersonically over land. To fix that, you probably need a tail more like is on the recently revealed Lockheed Skunk Works project.

So, can't use the Concorde engines or anything like them, and can't use the Concorde airframe economically (since most of the high-paying routes involve overland legs), but whatever turns out, I'm sure someone will say that they would have been better off if they just used Concordes with a new engine, and avionics, and structural materials, and . . .

The F-22 engine was most of the equation but the key point was the JP-8 +100 fuel that was developed to allow for the higher temperatures without having the fuel coke.

https://asmedigitalcollection.asme.org/energyresources/article-abstract/118/3/170/405906/JP-8-100-The-Development-of-High-Thermal-Stability?redirectedFrom=fulltext