The main kind of design we are familiar with is a top-down design, a goal-driven design process where results can be achieved through conscious planning and processes. This can be summed up as "if we see a watch, we infer a watchmaker". But there are bottom-up design processes too, where structure and function are emergent properties of the process - not of a conscious design. Cats know how to have sex, not how to grow a baby cat from a sea of chemicals.
The Ultimate 747 argument rests on the notion that top-down design requires a sufficient amount of complexity in order for there to be top-down design. A watch may be made by a watchmaker, but the watchmaker is something that needs accounting for too. And on top of that, the watchmaker has a big brain and spent time studying the craft in order to become a watchmaker. So given we know that the only top-down designers that we know themselves need further explanation, then if the universe was made by such a designer then that designer must too need to be explained.
Some theologians and philosophers counter that God requires no explanation, nor is God complex. That God is the ultimate simplicity, and that complexity only requires to material components. But in saying so, it misses the point of the exercise. If we define God as being the undesigned designer, it makes us wonder how that could possibly be the case. The only unaccounted design we know is emergent, and the top-down design in itself is never without explanation.
From what I can tell, the argument from design is left stripped of its power. Perhaps one could make the case that God's unaccounted nature is part of the definition of what it means to be God, and account for God's capacities through an ontological argument. But already the design analogy has lost its capacity. A unaccounted top-down designer is logically possible, but from what we know about design we just can't reasonably infer it and have good reason to be sceptical of such an argument.
Arguments from design for them to be useful must show top-down design, and not just through the absence of a bottom-up approach. Otherwise design arguments are going to have that problem of being completely counter to how we know design to be in nature. It's possible, but not worth considering.