TLDR: we can see it expanding
When light moves long distances it gets stretched out or compressed. This is called the Doppler effect, and it’s the same thing that causes an ambulance siren to raise and lower in pitch and is comes closer and then passes you.
For light this causes it to blue-shift or red-shift. Light from things moving towards us turns more blue, and stuff that’s moving away from us more Red.
Edwin Hubble (for whom the Hubble space telescope is named) catalogue distanced stars and Galaxies looking for Blue shift and Red Shift and discovered to his amazement that virtually EVERYTHING and in every direction is red shifted. He and other scientists concluded that the only possible explanation for this is that the universe is expanding and everything is moving further apart.
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