It seems this is a significant limitation of Unity’s timelines and animation processes.
They haven’t considered how animators actually work with “bezier” to construct their desired motions. Instead, they’ve done what’s easiest in terms of mathematics, and user interface, then told the marketing department to brag about having handles in the timeline editors. Yes, technically they’re handles, but they’re much more limiting than their equivalents in all other forms of commonly used animation software. It is, to some extent, false advertising to call these handles and harken to the manner they’re expected to be used in all other software.
Here’s a similar question, suffering from the same problem/limitation:
You can’t get a 90° tangent in Unity’s animation curve as it’s based on the tangent angle. Even the interpolation is based on cubic bezier curves you can not specify the control points manually, just the tangent. The actual control points will be calculated from that angle based on a 1/3 interval between the keytrames. If you want to know how they are calculated see my answer over here.
As i said a completely vertical tangent isn’t possible. It will result in an instant jump answer.
I you could specify the control points manually the curve wouldn’t represent a mathematical function anymore as the curve could curve back in time which wouldn’t make any sense. Why do you need such a steep increase? You most likely won’t even notice that first part as animations are sampled in time intervals.
This is a common curve in animation editing. After Effects, 3ds Max, Maya, etc all provide the ability to edit control points and their handles in this manner, as it creates a very desirable style of animation.
Mathematically, these are possible, as curves. And also quite common in frameworks like Core Animation and many other places where curves based on simple equations are made.
Here’s an example of an online tool that generates exactly this type of curve and what’s needed to use it in Core Animation: cubic-bezier.com