A great short story of how even the most basic astronomy techniques from the 1600s disprove the Young Earth hypothesis
Let's say we go back a few centuries when we don't have a ton of fancy astrological equipment, only basic telescopes and angle measuring devices.
How would you determine the distance from you, on the earth, to some astronomical object? Well, if that object is the sun, well if we're in the 1700s then we actually need to go back a century to 1672, when Cassini measured the distance between the earth and the sun using only basic angular measurements and basic geometry.
Here is a video that describes the process in detail, showing every mathematical step.They used something called parallax to determine the distance between them and Mars, and then used that to calculate distance to the Sun.
Interestingly enough, the use of parallax doesn't stop there. With more precise measurements, we can accurately determine the distance between us and a distant object.
The basic premise is this:
When we're on one side of the sun, we'll make a certain angle to the distant object, and when we're on the other side of the sun, that angle will be different. Using that angle difference, you can do some simple trigonometry to figure out the distance between the earth and that object.
However, this only works for certain angles. As the angle gets smaller it gets increasingly difficult to measure it. We can measure angles as tiny as 1/5000th of an arcsecond. (An arcsecond is 0.0002778 of a degree.)
However, this extremely primitive form of distance measurement is already a huge problem for the whole "universe is 6000 years old" claim, because 1/5000th of an arcsecond of parallax corresponds to a distance of 32,600 light years. That means that the light took 32,600 years to get to earth, completely shattering 6000yr number.
I could go on for some time about how this method was used to develop new, better methods for finding the distance to different objects (That works to much further distances) but I don't know if anyone really cares at all.