Well First of all he would have to be an entity that belongs to the physical world; ie: Made up of energy or some measurable substance. This would relegate him to the scientifically "Falsifiable" area. Now whether I would worship him or not is another matter altogether, but I will accept that he exists.
Which is what happened with the incarnation.
God became fully human and chose to be born in to this world.
The Bible records the events surrounding Jesus as historical facts.
The Bible is well supported by both Christian and non-Christian evidence. A number non-Christian scholars (in various fields) accept the evidence for the historical Jesus.
This evidence for Jesus is objective and therefore falsifiable...
In simple terms, this is the evidence for the existence of God.
If you say that you would "accept that he exists", by default you would be forced to embrace Theism.....presumably..??
Essentially, in a discussion like this (on existence of God/gods) from a Christian point-of-view it always ends up hinging of the evidence to support the events/ historical facts for Jesus, and the claims + proof of deity..
And this normally hinges on 2 creative acts of God that bookend the life of Jesus:
1) The virgin conception
2) The bodily resurrection (Jesus resurrected in to a new body)
Both of these things are totally unique, and if you want to attack Christianity and the concept of Jesus Christ as God, then this is normally what it hinges on.
People can debate the existence of God rationally and philosophically, but IMO the evidence comes from The Bible and the historical facts supporting the claims of Jesus, and the evidence of the creative acts that made him absolutely unique.....