Maya has no existence of its own.
Due its own adhyasa shakti , maya superimposes existence which is the svarupa of brahman, onto itself, so it has this borrowed superimposed existence, which is beginingless superimposition that gives it existence begininglessly.
Now with this existence maya makes brahman appear as nimitta karanam intelligent cause, and upadana karanam or material cause, both are this brahman due to the anirvachaniya maya.
Now when I say I am, there is already adhyasa of antakarana with brahman for jiva, and with maya for isvara.
When bhagavan projects the universe bhagavan who is pure brahman resorts to this maya shakti, this resorting in itself is adhyasa this is very well known to bhagavan, but knowing thus already he is resorting and projecting the universe and sustaining and resolving. He even knows that his maya has no real existence of its own either and yet its shakti he is able to use to resort to product a similar anirvachaniya jagat as well at the same time. So him asserting like in shruti the fact of manifestation maintenance and resolution does in no way make the creation a real creation, it remains adhyasa in and through all the way adhyasa alone, no other at all at any moment ever.
So with this adhyasta maya he is producer, maintainer , resolver . Its all adhyasta reality never actual.
Its mutual adhyasa, wherein the existence consciousness is appearing in maya and maya shakti is applied to brahman.