It’s actually not simple to determine the age of a given star. They are estimates based on indirect observations and/or rotation comparisons (rotation slows over time) using our sun as a baseline, since we do know its age pretty accurately. In the case of the sun, we can date really old rocks and extrapolate from that about how old the sun is.
Someone with more knowledge my be able to explain more clearly than me. But the larger issue is what ‘knowing’ means in science. Theories are tested through experimentation; observations are not.
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