Light bulbs, sex, internal combustion engines, radios, cd players, plumbing, the solar system, the space shuttle, the tides, Las Vegas, etc. Our existence and comfort is based on the predictability
of various processes and natural phenomena.
The archetypal experimental demonstration of determinism that anybody can do is to drop a small pebble into a smooth pool of water. The disturbance (wavefront) propagates away from its point(s) of origin. This is the fundamental dynamic of any and all disturbances in any and all media. It defines in a general and visualizable way what is meant by determinism.
Here's more evidence of determinism that can be extrapolated to relate to the underlying nature of our world:
Because the world of our experience offers so many examples (so much evidence) of determinism, it therefore makes sense to assume that the deeper reality is also deterministic.
Anyway, what's the alternative?