Can a god logically *know* that he/she/it exists?

This is of course Kant you are quoting.

In his 'Critique of Pure Reason' he makes a very similar speculation about God

But God is not a Being with separated thoughts. ANd existence gets its definition FROM Him. There are no outside 'things' that can pose a question to Him.

Now with us, 'existence' is something extracted from things truly outside us. But to God His entire being is actuality, no potentiality.

There are two kinds of being existed ,ie;as being existed as he/she/it ,as you call ,in a singular number and being existed because of the singular number existed.

So the first existence ,as a singular number,being existed with out any condition but the second existence with the condtion or condtions.

Having condition/s in this case means having their natures being design and fixed for them all.

For instance,the first energy that can perform work, being created by its Sole Creator in saying to nothingness ,Be and it is ,then this energy being used for igniting the big bang and then at that moment expand to be universe at the size of the space and then the space being filled in with mass ,from that one the Sole Creator melted these three entities in to time dimesion or the forth entity,being created in such a way that ,each one can not exist with out the others ,as being called exist with condition/s.

Because the Sole Creator let Himself being Known,through all HIS created things,then they all Know HIM by the nature that HE created for them all.

So logically speaking ,if the Sole Creator did not create the first energy that can perform work or being called as pure energy,as metion above ,then to be certain ,all created things, including human being,as having intellect ,then unable to become in existence and unable to know HIM because we are not existed.

So as GOD said ,there is no religion in those who do not use their intellect.

The mystery's of faith an GOD are beyond our ability to understand.