Everything that begins to exist has a cause
This is an unsupported assertion. How can you possibly know that EVERYTHING which begins to exist has a cause. Have you seen EVERYTHING in the universe? Furthermore, It does not follow logically that just because something exists, that it had a cause. It is entirely possible, logically speaking, that something could begin to exist without a cause. There is no logical contradiction in asserting this. In fact, we have pretty good evidence from quantum mechanics that certain particles flash in and out of existence without any cause whatsoever. So we also have direct evidence that things can exist without a cause, in addition to the fact that there is no logical contradiction which would make it impossible for something to exist without a cause.
There is overwhelming evidence that the universe began to exist
Okay let's break this statement down some. When we say that something "began to exist," this automatically implies the following: a period of time before the thing existed, a period of time during which the thing is coming not existence, and the period of time during which the thing exists. Now, scientists have said that the Big Bang was the beginning of the universe. But what is the universe? The universe, according to these same scientists, is the space-time continuum. That is, space and time are inseparable. The Big Bang was the beginning of both physical space AND the beginning of time. Therefore there was no time during which the universe did not exist. Therefore, the universe did not "begin to exist," because it ha existed at every point in time. Even if we accept that the universe "began to exist," it does not follow that it had a cause- see my reply to "everything that begins to exist has a cause."
and natural selection with respect to observed biological complexity has been sharply challenged
By who? 99.9 percent of scientists believe in evolution, no exaggeration.
Spiritual experience - you might as well say "subjective experience," which never counts as evidence for anything. Why? Because individuals are unreliable. Only by comparing evidence with others can we ever come to a justified conclusion about anything. So we can dismiss this argument immediately. But I do want to offer an alternative explanation for the cause of so called religious experiences.
Your own religious experience was the product of chemical reactions occurring in your brain. These chemical reactions seem to occur spontaneously in some individuals, but its been demonstrated that working oneself into a religious fervor can stimulate parts of the brain that lead to the so called "religious experience." Psychologists who have studied this phenomena have noted that the religious experience can be obtained in a number of ways. The most direct is to ingest psychedelic mushrooms or LSD. In one study they asked individuals who has taken LSD to record their experiences. They then compared these written accounts with the written accounts of those who had "authentic" religious experiences without the use of drugs. They then asked people to see if they could identify which account were written by those who had taken LSD and which accounts were written by those who had "authentic" experiences. The result? No one could tell the difference between the two groups- the accounts were indistinguishable from each other. Psychologists have speculated that religious experiences are caused by parts of the brain misfiring. It has also been noted that religious experiences (talking to God, angels, demons, etc.) are common among those who suffer from psychosis and/or schizophrenia.
the vast majority of new testament scholars will agree to these few facts
Yeah. Totally unbiased source, right? What about the vast majority of historians in general. The only real facts are that there was a person named Jesus, probably NOT born in Nazareth as it was a graveyard with a single house. Everything else is pure unsupported speculation.
There is actually good evidence that the entire story of Jesus was made up. Study the myth of Isis and Osiris, Persian Mithra, Horus, Hindu Krishna, etc. there are several stories, some thousands of years older than the Jesus story, which tell essentially the same story - demigod born of a virgin who is killed and then resurrected, travels around healing the sick, the blind, etc. it's a story that's been around for thousands of years prior to Jesus. The Jesus story is just one of the most recent iterations of this myth. People recycle this story because its a good story and it inspires people. But the fact that the same story existed thousands of years prior to Jesus cast doubt on the historical accuracy of the Jesus story.
Source: I'm a philosopher and have studied philosophy of religion. I've read the best arguments that christians have to offer from people like Craig and Plantiga and have found their arguments to be inadequate.