How far back could a 'modern' shark breed?

I keep seeing that stat that sharks have been on this Earth for hundreds of millions of years pretty much unchanged and are one of the most successful animals.

How far back in time could you take a currently alive shark and it could have viable offspring with the sharks then?

Any way to even know the answer? Educated guess? Wild guess?

If by breed you mean produce fertile offspring, AFAIK, animals can usually only “breed” within the same species, so once you go far enough back that your species disappears, I think you’re done. Just a wild ass guess.

It would be possible to get a decent estimate by analyzing the DNA of different modern sharks. But you’re still doing a lot of guesswork. I don’t think a lot of work has gone into determining which factors allow hybridization between currently existing species, where you could actually test a hypothesis with IVF. And any hypotheses about modern species breeding with long dead cousins (or distant ancestors) would be both untestable and possibly not of any scientific use.

This is true, but somewhat tautological. The OPs question could be rephrased as “How old are the actual modern shark species?” We can’t test if similar individuals in the fossil record could actually produce fertile offspring, so it isn’t a part of defining species in paleontology.

How easy is it to definitively determine the species of a fossiled shark?

Without DNA it’s pretty much impossible to determine definitively which animals belong to which species and can breed.

Don’t confuse this with being the same species since soft tissue is not preserved in fossils, only bones and I guess, cartilage.

A few million years back, at most:

However, it is now understood that the great white shark holds closer ties to the mako sharks and is descended from a separate lineage as a chronospecies unrelated to the mega-toothed sharks.[31] This was proven with the discovery of a transitional species that connected the great white to an unserrated shark known as Carcharodon hastalis.[35][36] This transitional species, which was named Carcharodon hubbelli in 2012, demonstrated a mosaic of evolutionary transitions between the great white and C. hastalis, namely the gradual appearance of serrations,[35] in a span of between 8 to 5 million years ago.[37] The progression of C. hubbelli characterized shifting diets and niches; by 6.5 million years ago, the serrations were developed enough for C. hubbelli to handle marine mammals.[35] Although both the great white and C. hastalis were known worldwide,[31] C. hubbelli is primarily found in California, Peru, Chile, and surrounding coastal deposits,[38] indicating that the great white had Pacific origins.[35] C. hastalis continued to thrive alongside the great white until its last appearance around one million years ago[39] and is believed to have possibly sired a number of additional species, including Carcharodon subserratus[31][35] and Carcharodon plicatilis.[31]

I’m confident it would be similar for other shark species.