The notion of 'intelligent design' raises more questions than it answers, and is fundamentally useless.
Our understanding of intelligence as we observe it, is that it is the product of biology - no intelligence has been observed that doesn't include biological systems in its generation.
Biology, we observe, requires some fairly specific conditions to arise. It needs an energy source; And it probably needs liquid water; A planetary body with a suitable mean temperature range; And for those conditions to persist in a fairly stable way for at least billions of years.
We know where the heavy elements that are required to make water and planets and all these things can come from - if you have enough hydrogen, it will, due to gravity, collect together in big lumps, and start to fuse under the pressure of its own weight.
If we start out by assuming the existence ONLY of protons and electrons, and the four forces of the Standard Model, then there is a clear and easily understood path from that situation, through at least two generations of stars, to planets some of which can support life, to planets with life, and then, via evolution, to the eventual emergence of intelligence.
From a big problem - "How does something as complex and strange as intelligence come to be?", we have answered the long series of such questions, and are now able to answer that question by appealing only to the far simpler question "How did something as simple as hydrogen come to be?".
Indeed, cosmologists even understand that - and are now left only with the question of how energy came to be, and how entropy came to be so low.
By contrast, 'Intelligent Design' takes the big problem - "How does something as complex and strange as intelligence come to be?", and says "Intelligence was required to make it happen". That's a fucking stupid non-answer.
If you asked me how to make a car, I could answer that by talking about sheet steel, alloy engine blocks, rubber tires, etc., and how to fit those things together. I could go back further, and explain how to mine iron ore, build blast furnaces, tap rubber from trees, and so on. The answer to the question is dependent on how simple the starting conditions are - are you building a car in an existing factory with existing supples of parts; Or do you need to build that factory, or make those parts?
What I could NOT get away with, while pretending to address the question, is starting with "First you need a car...".
Intelligent Design CANNOT answer the question 'Where did intelligence come from'. Not only is it not a good answer to the question; It's not an answer AT ALL.