There’s no need to bring the problem of evil into this discussion. We can just look at what is assumed as God’s responsibility and whether He is responsible for it or not. It seems like your argument is in the following form:
1. When God created human, he knew that:
a. He was creating beings with free will.
b. Beings with free will would use that free will to sin and/or to reject Him.
c. Most beings with free will would in fact use that free will to sin and/or to reject Him.
2. If God knew 1a, 1b, 1c, and still created human beings; then God is responsible for human’s behavior out of their free will, such as to sin or to reject Him.
3. God created human beings.
4. Therefore, God is responsible for consequences of human beings’ behaviors out of their free will, such as to sin or to reject Him.
Again, premise 1 seems to indicate that human beings are prone to sin or to reject God. For similar reason as I mentioned in the previous comment, such presumption is not true given that human beings were created with free will. Even if premise 1c were to be true, that most beings with free will would in fact use that free will to sin and/or to reject God, it does not attribute the cause nor the reason of sinning or rejecting God to God Himself. The ability to choose is given to human beings upon their creation, and the consequences of their choices were available for them to know; then it follows that human beings are aware of the consequences of their choices when choosing to behave in a certain way out of their free will. If this is true, (to put your robot example into the same argument form as your argument of God being responsible for human being’s rejection of Him), it follows that:
1. When your robot was choosing whether to murder people or not, he knew that:
a. He was made with free will.
b. He can choose to murder people, which will cause evil.
c. He can choose to not murder people, which will not cause evil.
2. If your robot knew 1a, 1b, 1c when he was choosing whether to murder people or not, and he still murdered people, then he would be responsible for the behavior out of his own free will, such as murdering people.
3. He still murdered people.
4. Your robot is responsible for the behavior out of his own free will, such as murdering people.
If human beings knew the consequences of their choices and then choose to behave in a certain way, then God, as the creator who has given human free will to choose, who is not the cause nor the reason for human to choose in a certain way, is not responsible for human beings’ behaviors out of their free will.