Imagine the lazy Fibonacci series. As long as you keep taking a number, the next one in the series is generated. It’s not incorrect to say it’s “potentially infinite”. And it exists, as the live algorithm that keeps cranking as long as you put in energy.
There must be a philosophical term for it but imho "potentially existing" (or having the potentiality of being constructed) is not the same thing as actually "existing" (in the reality that surrounds us).
Leaving aside the fact that we're not even sure numbers "exist", for better or worse, their "existence" is just us abstracting away some quantitates for different stuff (we've passed from counting cows or sheep on clay tablets 5000 years ago to believing that there could actually be an infinite number for us to count to).
And yes, I do believe there's a huge impedance mismatch between the world as we experience it around us and the different theoretical constructs that we now call physics or maths. I'm a Hume-ian, a guy who didn't take mathematical induction for granted (presumably not the Fibonacci series either).
