I made a graph trying to show the Sun's movement relative to the Galactic Plane. It doesn't seem to be correct I made a Desmos Graph following the most voted answer of this question, but I'm not sure if it is correct, because it suggest that the formation of the Sun happened shortly after it would have crossed the galactic plane, but the Sun did not exist before that. Is that possible?
Unfortunately, what you are trying to do is not possible. We do not know the details of the Sun's motion or the Galactic potential precisely enough to make a prediction of exactly where the Sun was 4.5 billion years ago.
The amplitude and period of the oscillatory motion that I specified in my answer to the previous question is known now to of order 10%. If you extrapolate backwards for more than a few cycles then the phase could be anything.
In addition, the Sun has likely changed its radial position in the Galaxy during its life. If so, then the amplitude and period of the vertical oscillatory motion will also have evolved.