That is not possible, as of now, in the Unity engine. You would need to handle it yourself. Take the Unity's Cinemachine package as an example. You can tweak the values of a cinemachine virtual camera in-game and store the values as you tweak them if you check the "Save during play". The package is designed in a way that it preserves its state, so when you stop playing, it doesn't lose the changes you made in play mode. Moreover, Cinemachine gives you gizmos that you can tweak the values through the game viewport, not only the inspector.

You would need to do such things for your game so when you start playing, you can, for example, click the gizmos on a puzzle object and change where it sits in the scene, and when you stop playing, the tweaked position would be preserved.