From the Wikipedia article on the Cosmic distance ladder:The cosmic distance ladder (also known as the Extragalactic Distance Scale) is the succession of methods by which astronomers determine the distances to celestial objects. A real direct distance measurement of an astronomical object is possible only for those objects that are close enough (within about a thousand parsecs) to Earth. The techniques for determining distances to more distant objects are all based on various measured correlations between methods that work at close distances with methods that work at larger distances. Several methods rely on a standard candle, which is an astronomical object that has a known luminosity.---------------This is similar to temperature scales where we use different devices for different ranges of temperature and evaluate how trustworthy they are by comparing them with methods that are trustworthy (have been proved).......
OTOH, science being open to new interpretations, if you have an alternative (falsifiable) explanation for the data we have, please produce it.
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We base our distance estimates on a series of different criteria. We *hope* that the assumptions we have made in using them are good ones.
From the Wikipedia article on the Cosmic distance ladder:
The cosmic distance ladder (also known as the Extragalactic Distance Scale) is the succession of methods by which astronomers determine the distances to celestial objects. A real direct distance measurement of an astronomical object is possible only for those objects that are "close enough" (within about a thousand parsecs) to Earth. The techniques for determining distances to more distant objects are all based on various measured correlations between methods that work at close distances with methods that work at larger distances. Several methods rely on a standard candle, which is an astronomical object that has a known luminosity.
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This is similar to temperature scales where we use different devices for different ranges of temperature and evaluate how trustworthy they are by comparing them with methods that are trustworthy (have been 'proved'). So we use parallax for objects close to Earth (and confirm by laser).
For a little bit more distant objects we use their brightness and have numerous comparisons with that method to parallax. We go on to method C, then D,... That's why it is called a ladder. Each method builds on the closer method. Astronomers are acutely aware of the assumptions they make when using them and generally are on the look-out for discrepancies.
The concept of "proof" is not really used in physical sciences because it involves context. Can you prove to a blind person that sight exists? That colors exist? Rather there is just an overwhelming abundance of evidence that cannot be ignored when using common sense.
We can see them, including the galaxy we live in. Don't know what you mean by proving the depths of what we call space.
There's these amazing things called "EYES". Check them out sometime - they allow you to see things so that you know they're there.
We can SEE them. Very simple. distance and movement can be proven by their Red Shift.
The fact we can sea them...
Along side tonnes of other proofs with things like red shift.
