How does NIST do a comparison that a particular algorithm is efficient and its security can not be broken by future quantum attacks?
How efficient an algorithm to implement is easy - these algorithms run on classical computers, and so people have made implementations of these algorithms, and it is straight-forward to measure the performance.
Security is measured by using the same method we use for non-quantum algorithms - people design the best cryptanalysis algorithms they can think of to break them, estimate running time of those cryptanalysis algorithms, and so we can select security parameters that make all such known cryptanalysis algorithms take an infeasible amount of time to run.
The only difference between a PQC and a non-PQC algorithm is that, for a PQC algorithm, we also consider cryptanalysis algorithms that run on a Quantum Computer. This is somewhat more tricky, because we don't have anything that can run a nontrivial cryptanalysis algorithm (the IBM quantum computer and similar are far too small, and are unable to perform the error correction needed), and quantum simulators (which run on classical computers) are also limited in the number of qubits they can handle. On the other hand, we really do have a good understanding on what operations a Quantum Computer can do, and so we can design algorithms that can run on a Quantum Computer. NIST doesn't do all this design work - the vast majority of this work is done by academics and cryptographers outside of NIST - NIST closely monitors this work, and takes this into account.