We can see 13.8 billion years into the past because the universe is expanding.
One way to reason about it is to think about being at the big bang 13.8 billion years ago. Draw a circle around yourself. Anything on the circle line is what happened exactly 13.8 billion years ago. Anything outside the circle is what happened earlier, and anything inside the circle is what happened after.
Because of the expansion of the universe, the circle gets bigger as time goes on.
Light from events outside the circle has already passed us and light from events inside the circle is still coming towards us.
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