How to blend from random idle spin to animation

Hi, using the animation features from unity is still somewhat new to me, so i need some help here:

Imagine having a cube (that is made up of 8 elements), that is supposed to spin infinitely around changing axis (randomized, smooth spin). When the cube gets activated, it should play a defined animation, which i imported from max (as a clip via FBX). The animation would require a fixed starting rotation from the cube, as the 8 elements would otherwise fly out in the wrong directions...

The imported animation itself works great...i just can't figure out a way on how to create the idle-state and blend between the idle and the final animation Creating a script to have the cube rotate smoothly around an altering axis is no problem, neither is having the imported animation play on some event...all done before... But how can i combine both way? Is it even possible?

Thanks in advance!