It was commented that a quick test flight doesn't pick up long term damage. But you don't need to be able to spot long term damage immediately. The point is that a progressive test program can be carried out. You don't need all the information at once. If you can send up aeroplanes and they don't show apparent damage in several hours flying, then you know that things can at least start moving again, even if you do engine inspections after every flight to start with - that would at least be something.
As confidence grows that there is no problem, you can return to the normal schedule. But if something comes up to make you suspect that there is a bigger problem (significant ash encounters, rising egt in a couple of aircraft from particular routes), then you take steps to find out what aircraft might also be affected and check them more intensively.
There is nothing about such a process which hasn't already been rehearsed with issues such as corrosion, cosmic rays, metal fatigue .... All it takes is somebody to write down an appropriately careful schedule. It isn't necessary to stop absolutely everything flying.
Exile from GROGGS