You don't need a quantum computer to break it, you just need a mathematical formula which could work for any number, and since private keys are numbers, finding such formula can solve any key by using even a mobile phone.
Humanity developing a quantum computer strong enough to break ECDSA seems far more likely than someone finding an effective alternative to Shor's algorithm for classical computing tho.
Now how did humanity invent computer? How did humanity invent quantum computer? I'm sure they were all humans working hard to obtain the necessary knowledge to invent such technologies. Whether it is more likely to have a strong QC or a simple math formula, that's debatable.
Given the hardness of the problem there seems to be a paradigm shift in mathematics required rather than a "simple math formula" though.
Don't get me wrong, I'm not saying that there is absolutely no way that somewhere out there is a solution to breaking ECDSA using consumer hardware, waiting to be discovered. I'm just saying that such an assertion is purely speculative since we have no reason to assume such a possibility given our current state of knowledge. Put differently, a breakthrough in mathematics that breaks ECDSA requires a lot more priors than a breakthrough in QC.
Humanity developing a quantum computer strong enough to break ECDSA seems far more likely than someone finding an effective alternative to Shor's algorithm for classical computing tho.
It is exactly the opposite. Quantum computers are likely never going to do any useful cryptography related stuff.
Maybe, but that does not necessarily make the opposite more likely. There's a third option after all: It may just not be possible. In the end we don't even know yet whether P=NP.