Analysis of Premise 1 of the Natural Argument of the Existence of God

Are premises 1 & 2 plausibly more true than false. First looking at premise 1 we may see and obvious objection. It may look in a form similar to this, “If everything that exists has an explanation for its existence, then what about God?” Obviously if this argument is for the existence of God then Christians believe that God is real and does exists. If the Christian response is that God exists with no explanation, then the obvious rebuttal to this would be that they would stop with the existence of the universe. So what’s a good response to this very valid question?
The objection however, is based on a misunderstanding. Remember this is based on Leibniz and his views and according to Leibniz there were things that must exist necessarily and those that are produced by an external cause. 
Things that exists necessarily simply exists by a necessity of their own nature. It’s impossible for them not to exists. What’s an example? Many mathematicians believe numbers must exist. They can’t cease in their existence. Something that has causes of their existence would something like a radio, planets, or galaxies. These all have causes of their existence that explain why they existence.
When Leibniz says everything that exists has an explanation of its existence. The explanation may be found in the necessity of its own nature or in the an external cause. So premise 1 could be expanded as such:
1. Everything that exists has an explanation of its existence either in the necessity of its own nature or in an external cause. 
Once we understand the premise better in its fulness the objection we’re considering here falls immediately. Because God here does have an explanation of his existence. That is that God exists namely by the necessity of his own nature. God exists necessarily, it’s impossible for him to fail to exists. Even Atheist must at least recognize this. It is simply impossible for God to have an external cause. It’s impossible for God to be caused by something outside of him. The explanation of God’s existence must therefore be that he exists by the necessity of his own nature. 
Leibniz’s argument is really an argument for the existence of God as a necessary uncaused being. The Atheist objection clarifies who God is in this instance. Therefore if God exists he is a necessarily existing uncaused being. 
So why think that Premise 1 is true? This is the second part of making sure the premise is a good part of a good argument. Here’s an illustration from philosopher Richard Taylor. 
Imagine you’re walking through the woods on a hike and you come across a translucent ball, lying on the forest floor. You would naturally wonder where the ball came from. If your hiking buddy said to you “Don’t worry about it, it just exist inexplicably” you would think he was either crazy or that he wanted you to just keep on moving. You wouldn’t take seriously that this ball just existed without any explanation of its existence. Suppose the ball was the size of an automobile instead. Increasing the size of the ball wouldn’t do anything to remove or satisfy a demand for an explanation for its existence. Suppose it were the size of a house, you would still have the same problem. If it were bigger than a planet or a galaxy you would still have the same problem. Suppose it were the size of a universe…same problem. Merely increasing the size of the object doesn’t do anything to remove or satisfy the need for an explanation of its existence.”
Thus I think it’s very plausible to think that everything that exists has an explanation of why it exists. 
Some atheist will say “This is true of everything ‘in’ the universe but not ‘of’ the universe.” This response is fallacious as philosopher atheist Arthur Schopenhauer remarks. “You cannot dismiss this principle enunciated in premise 1 like a hack when you’ve arrived at your desired destination. That would be arbitrary. You can’t just say that everything has an explanation of its existence then suddenly exempt the universe from this.”
Recall Leibniz does not make God an exception to Premise 1. This isn’t special pleading for God. The premise of Leibniz has universal applicability. It even applies to God. It is arbitrary for the Atheist to say the principle is true only then to dismiss it because they’ve arrived at the universe. 
The illustration of the ball is helpful because basically they have said “when the object gets very big it no longer needs an explanation.” Also notice how unscientific this response is to the argument. Modern Cosmology is devoted to an explanation of the universe. For them to respond that this wouldn’t apply to the universe is not only arbitrary but anyone thinking along these lines could never do science. They need some sort of justification to exempt the universe. 
This premise 1 is not like a law such as “gravity, thermodynamics, etc.” It’s not a physical principle operating within the universe. This is a metaphysical principle that applies to everything that exists. To being as being. Therefore it transcends or supersedes anything “of the universe” or “in the universe” as a whole. 

—based on Leibniz and Dr Craig lectures