@Metal-Brain
Whatever you say comrade. So how is your boss Putin doing these days anyway? Looks like his former cook is cooking Putin.
@divegeester
They do it analyzing the light intensity of 'standard candles', stars that have very similar light intensity outputs so using the inverse square law, they see star A has X intensity, and star B has half the intensity so they can use that fact to calculate how far away the dimmer star is and how red the light gets as it is further away in space and of course in time. So they notice the stars further away also are redder, which is what doppler shift does so they know that star is further away both from the intensity reading and the doppler shift. Between the two, they figure out how far away stuff is and it turns out Hubble figured out the further away they are the redder the light but the kind of star it is shows it is the same physics as nearer ones so they can get the distance and age. I hope that helps.
@divegeester
Cosmologists have just figure out time ran about 5 times slower in the early universe so there is that. Well, not THAT early, 1 billion years on.
https://www.space.com/quasar-clocks-universe-time-dilation