Well, I am assuming that you are familiar with the traditional or more philosophical proofs for the existence of God, since you mentioned the argument from design (which, while logically sound in my opinion, only gets you to a generic God and not a Christian one). But in addition to those, I offer you the following two syllogisms:
MAJOR PREMISE: Only God, if God exists, has the ability to accurately predict the future.
MINOR PREMISE: The future was accurately predicted in the Bible concerning the rise of the Roman Empire, the fate of other political entities, and the events in the life of Jesus Christ centuries before they occurred.
CONCLUSION: God exists.
And another:
MAJOR PREMISE: Only God, if God exists, has the ability to raise human beings from the dead.
MINOR PREMISE: Human beings have been raised from the dead.
CONCLUSION: God exists.
Both of your syllogisms are sterling examples of the logical fallacy of affirming the consequent, and are, sadly, invalid...
Even if I accept that humans have been raised from the dead and that the future has been predicted accurately, I'm not sure from where you obtained the premises that only God could be responsible for such things. While the arguments you offered are logically sound, they are meaningless unless you can demonstrate that their premises are true.