Can you elaborate? Im and Aero and while there is a defo a bunch of math involved suck, squeeze, bang, blow is pretty much the gist of how jet engines work and I don't find it really all that hand-wavy, its just a funny way of describing gas pressure and velocity graphs.
The compressor up front produces enough pressure to prevent the exhaust going out that way.
Another way to see it is you cannot start a turbine by dumping fuel in and igniting it. The turbine has to be spun up first, usually with an electric motor. The Me262 engines had an ingenious tiny gas engine in the nacelle which served that purpose, complete with a little handle to start it!
Next time you're on a jet, watch them do the engine start. You can see it slowly gaining speed, then suddenly it dramatically speeds up - that's when the fuel gets squirted in and ignited.
Anyhow, jet engines look deceptively simple. But they are real masterpieces of engineering.