If God would have to take the burden of CHANGINGS (like we people) than there would have been no importance of Salvation etc..
Change is not a 'burden' it is a asset - it allows the capacity to do things; to experience this 'permanent happiness' requires the capacity to change, because experience requires thought which requires change.
But, the one who has the abilty to go beyond Time and again step back into Time can see and define things physically, and as well as metaphorically with the reason of their existence, But after stepping into Time. Such people are called truely realized people in this world, These people are also known as true saints or guru's in this world.
As I stated earlier, it might be possible for entities to be outside of OUR time, but to be outside of time entirely (to be changeless) is to be utterly impotent, utter static - anything 'outside' of all time, is unable to 'step into time' (or do anything else for that matter), because that would be a CHANGE.
Indeed the movement from OUR time, to non time itself would logically require a change in the non time scope of existence - thus moving into a non-time scope would either need to create at least a single change in the existence of the contents of that scope (an instant of time denoting the entry into that scope) if not the continued capacity for change within that scope (time as it were) or else it would not be possible in the first place. If such a movement were possible, then in order to then 'step outside' that scope of existence, it would REQUIRE the capacity for change, as it would require the creation of 'before' and 'after' states (as mentioned in the earlier paragraph)
Yes, timeless god cannot, because if timeless God would have to take such burden, than there would have been no importance of Salvation, or Moksha, or Permanent libertation in this world
Sorry I just do not understand what you are trying to say