Is a deistic god possible?
No. Deductively, the claims of Deism (along with those of atheism and certain forms of polytheism) cannot possibly be true.
Deism is essentially the belief in the existence of a supreme creator who does not intervene in the universe and, more specifically, does not interact with humankind.
If a god like that existed, humans would be incapable of any kind of justified certainty, or true knowledge. Logic and reasoning would go out the window. We would and could have no reason to accept any fact over any falsehood.
If Deistic claims were true, human knowledge would be absolutely impossible.
Let's look at this in more detail.
An individual human, being merely one small piece in the cosmos and not the Creator of the universe, does not of himself have the authority to declare universal truths, like the law of non-contradiction. After all, he has no authority over the universe!
The law of non-contradiction states that nothing can both be and not be at the same time and in the same way. An acceptance of the absolute nature of this law is essential to any kind of coherent thought. Human infants are well aware of this law, even though they cannot articulate it. If this were not the case, infants would never learn anything at all. We all accept this law absolutely, yet we ourselves are not (and never have been) in any kind of position to establish this law. I certainly did not create the universe, and therefore I did not cause it to behave in a non-contradictory manner.
And neither did you.
Nonetheless, we all accept, at least from birth if not before, that the law of non-contradiction is inviolate. We accept this not on the basis of evidence, since evidence only makes sense if the law of non-contradiction is already presupposed. Otherwise, evidence may be identical to non-evidence, and we would have no way of knowing the difference.
The law of non-contradiction is part of the necessary groundwork for both deductive and inductive thought (including the inductive use of the scientific method). We all know this law with absolute certainty before we learn anything at all. We don't just think it's true -- we absolutely know it is true. If this were not the case, all of our conclusions -- every single one of them -- about anything whatsoever would be completely and utterly unjustified.
Where does this specific knowledge regarding the non-contradictory nature of not only the comprehensive universe, but of every element in, and of every facet of, the comprehensive universe, come from?
If this presupposition, this initial belief regarding the nature of the entire universe, is the product of anything other than a reasoning mind, it is without intelligent reason, without logical grounds, without rational justification. If it is not guided by an intending and coordinating mind, it can only be said to be random (or uncoordinated) and accidental (or unintentional). If every human being's starting belief or presupposition that reality is non-contradictory were a belief that was merely accidental and random, without any reasoned or logical justification whatsoever, it would be by definition irrational, and so would be every single conclusion based on it.
Are all of your conclusions irrational?
For our conclusions to not be irrational -- absolutely any of our conclusions at all -- we must individually be specially and directly informed by the personal Creator of the universe that He Himself is perfectly non-contradictory (2 Timothy 2:13). If He Himself is non-contradictory, then what He creates, He creates. Nothing that is made could be not-made. The law of non-contradiction would thereby be rationally established universally, because it describes the Creator of the universe, and, if said God is incapable of lying (Titus 1:2; Hebrews 6:18) and is also the cause of all things (John 1:3; 1 Corinthians 8:6; Colossians 1:16), we are then rationally justified in accepting the law of non-contradiction as being applicable to the entire universe, and all of our conclusions that presuppose such a thing could also be rational.
But this is the only possible way that any of our conclusions can be rationally justified.
If God does not directly communicate with every single human, informing them of His own power and non-contradictory nature (Romans 1:19-20), our use of reason is absolutely unreasonable.
Therefore, if Deistic claims are true, it is impossible for humans to reason. This makes the claims of Deism deductively false.
What would you say to members of Islamic State and al-Qaeda?
Do you believe that a human can voluntarily turn to god of her own will?
What is the source of moral obligation?
Why do atheists embrace the notion that non-existence can have any causal relationship with existence?
If God condemned people to Hell because of free will, yet He wanted to save them, would that mean He isn't capable of saving them?