 

Always existing and being the source of the existence of all other beings
is not problematic.

But, as you put, Being the source of "all" existence, including one's own,
would mean that God came from nothing, a concept alien to Christianity and
Theism.  It is better to understand the classical concepts of Necessary and
Contingent existence.  God exists necessarily, always.  God created
contingent beings.  This is a coherent solution to existence, so long as
the concept of God is coherent.
 

Not a very good answer.  If reason cannot by any means understand something
then it is likely that "it" is a null concept, something not in reality.