Probably the same way everyone does, by pulling it out of thin air as a guess. When nobody even knows what theoretical breakthroughs are necessary, you'll always end up with a scattershot all over the place, even amongst experts. Try asking working mathematicians how long until the Riemann hypothesis is resolved one way or another, or look at what people were saying about Fermat's Last Theorem up until it was solved.

What we do know is that current techniques won't get us close to AGI, so something new is needed (or perhaps like backprop, something old will work once we have enough compute power). Personally I'm bullish on AGI because I have strikingly low faith in the ability of evolution to operate very effectively as a tool for algorithm discovery, so I suspect that once we've hit the compute threshold we'll find that many different algorithms can do the trick, and 40 years is probably not out of the question for us to hit that point (or 10, or 100), depending who you talk to about what the compute threshold might be.

I'd caution against putting too much weight in what experts say, though, since with a tiny few set of exceptions anyone working on "AI" today is actually just working on narrow AI, which is, as someone put it, just glorified linear regression. Those tools will almost certainly be part of the solution, but only in the sense that the classical theory of Diophantine equations was part of Weil's proof of Fermat's Last Theorem - they are not the core of the theoretical approach.