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.
How can I explain this better? Let me use time and space.
With current technology, you can not achieve anything remotely close to 1% of the speed of light, so you can't even think about the possibility of time travel.
But guess what? You can time travel by a different way, for example, whenever you look at the sun (hopefully indirectly) you are seeing around 8 minutes in the past, looking at stars will give you thousands and millions of years view of the past, now imagine that all the knowledge and information already exist, we can't just access them all at once. If you don't believe me, do some research on dejavu, something we all have experienced in our lives.
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.