One could as well ask the reverse.
What would you do if the Christian God was proved?
What I would do is do what I've always done, which is to listen to my conscience.
I'm not doing what I hope is morally upright based on one or the other.
Now if someone were to ask me if God told me to go sacrifice my son as a burnt offering on a mountain a three days journey away, and I knew for a fact it was God asking me to do this thing, I'd have to decline. An evil act is an evil act no matter who is asking it of me.
Unless I have more information than is explicitly recorded in the Bible which is the obviously the Sacrifice of Isaac.
For the purpose of examining the very hotly disputed event which superficially seems barbaric to ask of a loving father, I'll go on a bit.
Now some might say and I might agree that God's nature is good. That agreed to, I could still not simply comply without asking a lot of questions.
It may very well be that there was an exchange of this sort between Abraham and God, but this is not recorded. Paul, in one view is speculating on the possible thoughts entertained by Abraham relative to this situation when he writes about this - "19 He considered that God was able even to raise him from the dead, from which, figuratively speaking, he did receive him back." Hebrews 11:19 ESV.
Nowhere in the Hebrew Scriptures is this explicitly stated. Now I'm not arguing that Paul got this wrong, just that we would have to intuit the mindset of Abraham ,or have the witness of the Holy Spirit to the truth of this, or admit that everything penned by Paul when he writes is 100% spot on (even though in his letters he speaks numerous times that this is his "opinion" and "I think I have God's spirit".
We can make a choice about what we'll be willing to choose to believe.
It also must be noted that much has not been written about things said and done by Jesus as well - see John 21:25 - "25 Now there are also many other things that Jesus did. Were every one of them to be written, I suppose that the world itself could not contain the books that would be written." - ESV.
This means I have a choice about how to interpret what Abraham did and what he knew and any conversations he may or may not have had with God. (or even that matter with Isaac...see Genesis 22:8 "Abraham said, “God will provide for himself the lamb for a burnt offering, my son.” So they went both of them together." In that latter portion..."So they went both of them together" is pregnant with meaning. What if any conversation occurred? We don't know.
Absence of evidence isn't evidence of absence.
Again I have a choice. It's not forced on me so that I have no choice as to which explanation I'll act on.
I prefer to "Let God be true, though every man a liar" - Romans 3:4
Also "Now faith is the assurance of things hoped for, the conviction of things not seen." - Hebrews 11:1
I have assurance because I hope.
So one might ask that this business of faith isn't a simple binary transaction, such that one could answer this "What would you do if it were proven to you beyond a shadow of a doubt that your wife was a faithless harlot, who never loved you or her children" in a simple way.
You would be horrified, and you would fight tooth and nail not to establish the truth of such terrible accusations. If you loved your wife you would do all you could to maintain the relationship you've built up over the years and you would hold in abeyance the challenges to her integrity.
Think of Jobs so-called "comforters". Job had little to go on w/regard to his sufferings during the ordeal. His integrity was challenged, his family was murdered by Satan, his health fled, his wife told him to curse God and die. But...in the end he had witness borne to him that his faith was not in vain.