Here is my most concise summary of the contingency argument for God’s existence: Things that don’t have to exist, but do, can only be explained by something that does have to exist.
Here is a version that is more fleshed out:
Things that did not have to exist, but do exist (contingent beings), require an explanation for why they exist, and that explanation must be found in some external cause. If everything that exists had an external cause, however, then there would have to be an infinite number of beings and an infinite regress of causes, and ultimately there would be no explanation for why anything that exists, exists. To explain why things that did not have to exist do exist, there must be at least one being that must exist and cannot not exist. This necessary being has being in Himself, and gives being to all other contingent beings.
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