system
Given the following post, respond as if you're commenting on Reddit:
human
How did scientists estimate the age of Earth before the advent of radiometric dating?
gpt
There were a lot of different attempts that largely relied on estimating the rate of something and then extrapolating that to estimate the age of the Earth, i.e. there is Y quantity of this, it changes at X rate today, we'll assume it started at Z condition has always occurred at X rate and from there we can estimate how long the process has been happening. Some notable examples/categories:

A variety of people used the generations of people discussed in the christian bible and some estimation of the average lifespan to estimate when the world was created (e.g. Kepler, Ussher, Lightfoot). These kind of border on scientific since even though they were based on a religious text, they were applying a form of logic to try to use said text to make an estimate.

A common, more clearly scientific, pre-radiometric dating way to estimate the age of the Earth was from cooling rates. Assuming that the Earth started out molten and knowing something about cooling rates of various materials, you can estimate how long it would take for a body the size of the Earth to cool (with some big assumptions). Notable examples of this were undertaken by Comte de Buffon and Lord Kelvin (and both Newton and Liebniz kind of dabbled in this, but weren't as direct in terms of actually producing a formal estimate of the age). 

Another common attempt was using the salinity of the ocean (the so-called "salt accumulation clock"), i.e. we know the salinity of the ocean on average, we can measure the rate at which salts are delivered to the ocean via rivers, and if we assume the ocean started off as entirely fresh water, we can estimate how long it would take to build the salt concentration we observe. A variety of people did these types of calculations, including Edmund Halley (same Halley as the comet), T. Mellard Reade, and John Joly. 

There were estimates made based on orbital mechanics and dissipation of tidal friction between the Earth and Moon. George Darwin (son of Charles Darwin) and Lord Kelvin both used these lines of reasoning to estimate the age of the Earth.

The most consistent mechanism across history though was trying to use the thickness of sedimentary rocks to estimate how long it took for them to accumulate. The Greek historian Herodotus presented some estimations based on sediment deposition rates of the Nile. There were a flurry of these types of estimations in the late 1800s with one of the most complex being put together by Charles Walcott. Other notable estimations using this technique came from J.D. Dana and others.

Pretty much all of these estimation techniques missed the mark by at least a few billion years, largely because of incomplete understanding of the processes (e.g. heat from radioactivity dramatically changes the cooling rate of the Earth, non steady delivery of salts to the ocean plus a variety of mechanisms for dissolved loads to be removed / sequestered, or that the sedimentary record includes lots of gaps of erosion and non-deposition, etc). There are lots of sources out there that go through much of this in a lot of detail, the above was mostly taken from the introductory chapter of the "Geochronology and Thermochronology" textbook by Reiners et al.