The Doctrine of the Trinity is not itself logically provable. I am willing to consider the possibility that it might even be wrong. It is at best an attempt to reconcile seemingly irreconcilably contradictory scriptural statements regarding the nature of the Godhead as illuminated by Old and New Testament writings. We believe that scripture is not wildly contradictory and can therefore be logically reconciled by the adoption of the Trinitarian Nature of God. It works for us. Personally I am quite content to wait and see what God is really like until I am face to face with him.
You however have no such need to reconcile seemingly contradictory scriptural statements. You would simply say God does not exist and scripture is a load of contradictory bunk. (Problem solved), as far as you are concerned.
But WE can’t leave it there because some of us have had personal experience of ‘God’, sufficient to cause us to be willing to regulate our lives as a result of it, in the light of what scripture would have us believe we need to do.
Each believers experience of God is usually of such a subjective and personal nature that you would find it singularly unconvincing. That is a matter of personal judgement and choice.
Like it or not we each have to make our own choice in these matters. You make yours, I make mine, based on our individual experiences. Hopefully we can respect eachothers point of view hoping it to be based on honest consideration of such facts as we each respectively have.