How do we know that distant stars and galaxies are real?

In some universe,with physical laws the same as in ours, our world is some kind of "lab environment". Our solar system is enclosed in a balloon-like sphere with a radius of a few light-days around the sun (just big enough to contain Oort clouds and all long-period comets).

The inner side of the sphere is a holographic screen/Wave/particle emitter that displays distant stars and galaxies (which would solve parallax observations?).

What else do I need to take into consideration to make it scientifically accurate? What about background radiation?

How could inhabitants detect such a setting without actually going to the "Truman Show wall"?

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How do we know that distant stars and galaxies are real?

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