On what logical or rhetorical basis do you get to shift the burden of proof away from the person making the original argument?
We both approach the subject from our own world views. Some aspects of our existence are problematic for one world view but not another.
For example, the concept "before time" is used althoug meaningless to the secular materialist, but not to the creationist.
Another example would be the existence of matter, energy and information. Again not a problem to the creationist, but a migraine for the secular materialist.
The problems are due to world view assumptions. Creationists are allowed to "assume" a Creator (even though we have good evidence we will call it an assumption for now). Since we assume a Creator, that Creator is not limited nor can be logically limited by the materialist world view.
This is rather basic and should be relatively simple to comprehend; that the universe was created means de facto that the Creator not only exists outside the universe but before the universe. It also follows that the creation of the universe and its laws must necessarily be a subset of essential existence and its laws.
So the original question, "Who designed the Designer?" makes certain assumptions that are tied to the materialist world view, such as everything is subject to the laws of the universe. That's baggage from your world view, as I said and the question only seems to make sense so long as the invalid assumptions from the baggage are in place.