You started by asking for a synonym for "Non-existent/Non-existence". So in the context of your quote, we could say:
Today, the Idea of God's existence is as unbelievable as God's absence.
However, you also asked for a "technical term", so in light of that it might be better to reword as:
For many, the idea of God's existence is as unpopular today as atheism once was."
I used "unpopular" rather than "unbelievable" because I suggest you at least consider using "unpopular" instead. I'll leave it to you to compare the meanings of these two words.
I think it is important to mention that "the idea of God's non-existence" has been around as long as "the idea of God's existence" in terms of what we know from discovered written history. Both ideas were considered "unbelievable" during certain periods by specific cultures. There is documented evidence for both theism and atheism in various cultures as far back as such writings have been found and dated.