re: No matter what direction we point a telescope, we always look toward the Big Bang - why?

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Believing that radiation/energy was always there to spontaneously generate matter and anti-matter to form the universe is an interesting theory, but we can't pretend it's more plausible than an uneducated person's belief that something supernatural caused the universe's expansion. In the end, both ideas require a measure of faith.

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Energy spontaneously coming into existence was predicted by science and has likely been proved.

If you move two uncharged plates close enough together in a vacuum they experience an attractive force. This is called the Casimir effect and has been observed many times. Overwhelming evidence points to this being a result of particles popping in and out of existence in a vacuum.

This means that what you think of as empty space is actually a bubbling foam of very low level energy where particles are constantly popping in and out of existence. I know this does not sound intuitive but neither does the fact that what we think of as solid objects like rocks and tables are really made of fogs of electrons.

There are speculative theories where the math shows that a bubble of particles in "empty" space can spontaneously inflate to the size of our universe but there's much to be proved about that.