Youâ€™re asking â€śWhere along the line of the Y axis of my object does it intersect the XY plane of its parent?â€ť. The google term is â€śLine Plane Intersectionâ€ť
Thereâ€™s a couple main ideas to make this possible:

If you make a line thatâ€™s perpendicular to the plane, then any other line thatâ€™s perpendicular to that line MUST be exactly on the plane.

The dot product of 2 vectors is 0 if and only if theyâ€™re perpendicular

If you have a point and a direction vector, that point plus some random multiple of the direction gives you a new point on a line.
Using those 3 ideas together: If we move some multiple of a direction from our starting point, and dot that with the normal, and it equals 0, then weâ€™re on the plane.
Using that we can make an equation, which we can directly solve for that â€śsome multipleâ€ť, which you can add to the Y translation to get to the plane.
I donâ€™t have time today to give you a FULL writeup â€¦ so I just googled it and found a Stack Overflow answer that seems worth trying 3D LinePlane Intersection  Stack Overflow
And just a little optimization you can do: the vector u
in the SO answer is equal to the second row of the matrix of your object divided by the Y scale value.