>I took QFT some years back and it also went over my head. There is still that mental gap of where the only way you can think about time is via time-(in)dependent wave function.
Total bullshit. The wave function is time dependent.
Given psi(x, t), if the relation between x and t is not non- linear. Then you can have a time-independent Schrodinger equation with a time-independent wave-function i.e psi(x).
However, you do not need start with a time dependent wave function to justify the time-independent wave function.
Total bullshit. The wave function is time dependent.