I would believe in God if...

[Nonpareil]

Very good question!  Philosophically speaking randomness, chance, and throwing things together without a purpose would result in chaos and a pile of stuff.

Not entirely true.

Even assuming that everything was entirely random (and it's demonstrably not), it would still be entirely possible to have sections - even very large sections - could appear ordered within themselves. Infinite monkeys, infinite typewriters, and all that; in an infinite sample size of random results, not only is it possible to have some of them turn out looking ordered, it is necessary.

Beyond that, the universe isn't random (or, at least, not entirely - getting into quantum mechanics is not feasible for a discussion like this, and doesn't actually affect anything regardless). It obeys laws, and is ordered. This does not require, or even begin to imply, that the universe has "purpose".

The universe, its basic building blocks, the extreme diversity of life, and its building blocks, appear to have complicated structures designed into them at their basic levels.  I believe this argument is partly known as irreducible complexity.

Irreducible complexity is a nonsense concept, I'm afraid. Even setting aside its incoherent and rather fuzzily-defined nature, there have been exactly zero examples of any structure that has been shown to be irreducibly complex.

Note that this does not mean that all structures are yet explained, but "we don't know how it got that way yet" is not equivalent to "it is irreducibly complex".