Can a non-response to a vaccine be tested?
You can test for antibody titers (and also connected memory) for the persons who got the vaccine and then decide, if these antibody levels are protective or not. Problem with this method is, that it is not clear, what levels are protective. There is still no experience with it for SARS-CoV-2, this is routinely done for other diseases.
According to clinicaltrials.gov, the study design is a placebo controlled trial triple blinded (Participant, Care Provider, Investigator) which enables the direct comparision of the vaccine arm with the placebo arm. Here you analyze the difference between these arms. If the vaccine delivers a sufficient protection, less (or ideally no) people in the vaccine arm get sick - which is exactly what was observed.
A last possibility would be to challenge people, who received the test vaccine with the virus and see, if they develop the disease. However, this approach is highly unethical since you possibly infect a large number of people with a potentially deadly virus, when the vaccine does not work. I doubt that a researcher who wants to do this will get clearance for these experiments by the internal review boards involved in these trials.
This is done in earlier stages in animal experiments, to challenge the immune response.