I answered a similar question a few weeks back so I'm mostly just gonna copy/paste that

But TL;DR- Yes, we'd still have radiometric dating, arguably it would be less complicated since we wouldn't need to account for nuclear testing and the bombs dropped on Japan messing with the ratio of different isotopes found in nature, but it does also offer some new opportunities for dating certain things. For example, since we started setting off nuclear bombs basically all steel we've made has been a tiny bit radioactive, so you can pretty reliably date steel to being from before or after WWII based on the presence of radioactive contaminants. (Those traces of radioactive material are pretty harmless and don't affect things for most applications, but there are certain cases where it is actually very important so there's a market for recycling WWII battle ships and such to get steel that's free of radioactive contaminants)

There are 3 naturally occuring types of carbon, called isotopes, ¹²C, ¹³C, and ¹⁴C. These are all basically the same except for the number of neutrons in the nucleus of the atom. Living things can use all 3 types to build sugars and proteins and all those other organic molecules needed for life. Animals get it from the food they eat, plants get it from the air. These 3 isotopes all exist in nature in a pretty consistent ratio

¹⁴C, however, is unstable (radioactive) and over time decays into more stable elements.

But it also is constantly getting replenished from cosmic rays interacting with other gases in the atmosphere making more, so as long as something is alive the ratio of carbon 14 in that plant or animal to the other types of carbon stays pretty consistent. It breathes/poops out carbon and takes more in, keeping that ratio pretty consistent.

But once it dies, it's not taking any new carbon in, so what was there when it died is all it's ever going to have until it decomposes away entirely or gets eaten by scavengers or whatever. The ¹²C and ¹³C are basically going to stay put, while the ¹⁴C slowly decays.

So to date something you just need to look at the ratio of the different types of carbon and you can figure out how old it is.

Let's say ¹⁴C has a half life (the time it takes for half of it to decay) of 1 year (its actually something like 5 or 6 thousand years but this makes the math easy with smaller, easier to digest numbers)

And let's say the ratio is 1:1, ¹²C+¹³C to ¹⁴C (again, it's more like 1% carbon 14 IRL)

So after a year, half of the ¹⁴C will be gone, and the ratio will be 2:1

After another year half of that remaining ¹⁴C will be gone and it'll be a 4:1 ratio, another year and it's 8:1, etc.

This of course has limitations. After a long enough time basically all of the carbon 14 will be gone and you can't really date things that way anymore. I think the limit is something like 50,000 years.

It's also only really useful for plants, animals, and stuff made from them (leather, textiles, the straw in mud brick buildings, food, etc.) so not particularly useful for dating inorganic matter.

There's also a few things that can cause more ¹⁴C to form than normal, humans caused one with our nuclear testing, there was another event around the 8th century that we've discovered from measuring the carbon 14 in tree rings from that time that we think may have been caused by a supernova sending more cosmic rays our way than usual. So those events also need to be accounted for.

But there's other similar techniques using elements with longer half lives that we can use to date older or inorganic materials.

For example uranium-lead dating. When the mineral Zircon forms, it tends to include uranium but exclude lead. But over time uranium decays into lead, so if you have a sample of zircon, you can measure how much lead is in it and figure out how long ago it must have formed because that lead must have once been uranium that has decayed at a steady pace over the centuries.