Yes. They could only exist if they were the product of his deliberate design. Moreover, all the effects of sin could only exist if God designed the universe so as to produce those effects, thus they must also be his fault.
Take just one example: lust. Lust is the basis for many sins. If we did not experience lust, we would not commit any of its related sins.
Science has proven that lust is hardwired into the brain: it exists there as a fundamental component of the actual design of the human brain and body. So if God designed that brain and body, he must have consciously and deliberately programmed it to experience and be motivated by lust. Yet there is no credible reason for any intelligent designer to program our brains to feel lust. Lust serves no intelligent purpose. We don't need it to experience love. We love friends, neighbors, and family without experiencing lust; even love for our spouses isn't produced by lust, but respect and admiration and compassion. And we don't need lust for procreation. Most life on earth reproduces without even brains, much less the means to experience lust. God could have designed the universe so that love between a man and a woman spontaneously generates a child.
However, evolution by natural selection (in other words, the complete absence of a compassionate and intelligent designer) explains why our brains are programmed to feel lust. Indeed, it is the only plausible explanation of that fact. As a product of God's design, it makes no sense at all. But as such a product, God shares responsibility for all the sins motivated by the lust that he installed in our brains.