Clone character with new character's animator playing at the same transition position

Hi. I know how to sync cloned character's animator with original character only when the original character's animator isn't in transition (using animator.Play(stateName, layer, normalizedTime)). But the problem is when cloning/instantiating happens while the original animator is in transition. I tried playing with Animator.CrossFade but the problem here is that the CrossFade transition allways starts at normalized time 0 and plays the whole transitions so the characters aren't synced at first, but eventually get synced, which is not good for me. Is there any solution/workaround for this situation?