The most convincing proof is a load test that simulates the real number of users, jobs and devices, including the busy periods like shift changes and turnarounds when activity spikes. Results should show response times and error rates under that load, not just whether the system stayed up.
References from customers running at a similar scale also help, since real use often finds problems that tests miss. A sensible rollout plan adds load in stages, so performance can be checked at each step before the next group of sites or crews goes live.