How to make an animation start from an unknown state?

Let’s say that I have an animation currently or previously running, affecting the position or rotation X, Y or Z of a game object. Something occurs and an animation may have been stopped / interrupted (and this is fine). The point is that the position and rotation are in at least degree unknown at the moment (unless I grab the information from the transform myself).
Now I want to make the game object follow a new animation. I want the game object to start from where ever it is, and I have properties set for where it should end up. I indicate this to the animator by not having a key frame at 0. I’ve told the animator not to write defaults.

It still happens. So for example if I have a 2-second long animation with a particular rotation only on the last key frame, and no key frames prior, at t=0 it will just set the rotation to the value specified by the last key frame. This is a jarring transition and certainly not an animated one!

I know I can solve this in code, manually animating the object to a known start state for an animation clip, I am just trying to minimize the amount of coding done when other tools are available Is there a way with animations alone to do this?

Thanks