How do you figure out fuel specific impulse non-experimentally?
The relevant property is the temperature of the burnt fuel when it leaves the rocket engine nozzle, i.e. when it stops exchanging impulse with the engine.

That temperature you can convert into a velocity distribution of the gas particles, multiply with their molar mass, and that's it. (somewhat less than that of course, because no all gas particles are flying in the exact same direction. depends on the nozzle type, among other influences)

The temperature you can estimate to some extent from the reaction enthalpy, but of course you have radiative and conductive losses. Which is where this becomes an engineering problem.