Age estimation is a tricky thing - there are no brass labels on distant galaxies showing their age, or if there are, the letters are too small to see. There are several different methods, and while there’s some disagreement between them, it’s on the magnitude of 0.1Gyr, not 13.7+/-13.
Wikipedia is a good starting point: https://en.m.wikipedia.org/wiki/Age_of_the_universe . I’m not an expert on the topic, but if I’d like to dig deeper, I’d visit Amazon, look for cosmology books, pick something that’s expansive, looks like a textbook, plus point if the title contains the word ‘introduction’ (you’ll see the irony inside). It’s the best if you find something from after 2010 (after Planck and WMAP missions). I found Weinberg: Cosmology, but that’s from 2008. If you have your favorite textbook, check it out from the local library, but make sure NOT to download it from Library Genesis (http://libgen.is/ is the site to avoid) because that would cause the publisher financial losses.