I'll try to add some clarification on some common misunderstandings.
The creationist/ ID design argument is not that: "any type of complexity or intelligence in existence needed a designer". Which would of course logically require any complex or intelligent creator to themself have needed a creator.
But instead the argument is (for example): "The origin of complexity [complex systems composed of specified componet parts] from non-complexity requires, or is best explained as the result of intelligent design." Or "an intelligent designer is necessary for the origin of life from non-life" etc. There is no logical requirement in these arguments for the designer to themself also have an origin, (or even be composed of componet parts), hense no need according to the same argument for the designer to also have had a designer.
(The argument is then also supported by design theorists with specific scientific and observational evidence.)