The analogy is bad because it is perfectly possible to assemble a puzzle with pure trail and error and no intelligence at all. The physical nature of the pieces is such that they fit (shape and color) or not. Any mechanism which allows for that trail and error can solve it without any intelligence.
The evolutionary model describes just such a mechanism for biological organisms. That is huge numbers of trails are made; many, many errors and some successes which are "kept" just as puzzle pieces that fit are kept.
Your analogy is not useful in any way to attack the evolutionary model.