No, we observe what are believed to be the results of the big bang, or more accurately, the current state of the universe (well, implied by the light that reaches Earth) based on a theory about its origins - the big bang.

: With ever-increasing-fidelity telescopes. besides which
: nothing is ever proven in science. That's not how it works.

Repeatable demonstration is proof that in specific conditions, given specific actions, a specific result occurs. We form laws based on such experimentation.

Per your next couple of paragraphs, from Wiki: "A scientific law is a statement based on repeated experimental observations that describes some aspect of the world. A scientific law always applies under the same conditions, and implies that there is a causal relationship involving its elements."

: This is all science strives to achieve...a theory is the best explanation
: possible to explain the observed facts.

Precisely.

: Not quite the same. Looking at a childhood photo of yourself is not looking
: at you in the past but looking at a photograph in the present that was
: taken in the past.

That is precisely what a photon is that arrives at Earth which was launched from its source long ago.

: If you look at the star Epsilon Eridani (let's bring
: Halo back to the discussion) you are not seeing in its present state nor
: can you ever unless you travel there. From Earth, the best you can see is
: what Epsilon Eridani looked like 10.5 years ago. That's all I mean by
: looking into the past. Looking at the light striking your eye when looking
: at that star is not seeing it as it presently is.

That's exactly what I said.

: I guess I see that as the same thing.
: It wasn't intended as a cop-out.

Ok, but I see there is a significant difference. What you are fundamentally seeing is not "the past", but a photon that, presuming it is unchanged entirely since the moment it was given its properties, is a snapshot of the state of it source when it was launched. There's no time travel. There's only that photon.

: If scientists created life from non-life in
: the lab, contamination would be the first suspect because life is so
: prolific.

Sure

: It's not a belief of mine, just the most reasonable place to start to find an
: answer. Everything that has ever occurred that has been figured out has
: had a natural explanation behind it.

Because every method we use to explore is bound to the natural world :) So our explanations of observed natural phenomena can only acceptably, and fundamentally, be naturalistic.

: Science only deals with natural
: explanations because what would be the alternative?
: "Super"natural? What is that? How can it be brought to bear on
: the repeatability and testability of experiments.

Exactly.

: The total number of verifiable supernatural events that have definitively
: occurred in the history of the world is still zero, is it not? Sure, there
: were things that used to be called supernatural like lightning, eclipses,
: tornadoes, earthquakes, comets. Those were really supernatural in the days
: when how those phenomena manifested themselves was not known. Now they are
: known and have sound natural explanations for their existence. In fact,
: everything we 'know' has a natural explanation.

Exactly.
We used natural methods to explore natural phenomena, and as our scientific capabilities and curiosity has grown, so has our understanding of the natural world.

: There are things we don't know, such as how the chemistry of life came from
: the chemistry of non-life.

I really need to start marking comments these for quotables :P

: Given everything we've ever figured out before,
: the best place to start is look for a natural explanation. How could you
: begin otherwise?

I completely agree. Since scientific processes can only observe in the natural realm (regardless of whether one believes there is a supernatural realm or not), then our discoveries and explanations of natural phenomena can and only ever will be entirely natural in origin.

Jumping back, here's a quote from a skeptic website I think is relevant, regarding the difference (or lack thereof) between historical and operational science - and yet the result makes clear the difference:

Today, atmospheric scientists can directly measure the composition of the atmosphere – from ground based measurements to planes carrying instruments which suck in some air and analyze it. They can then develop models which can tell us how air packets flow from one region of the Earth to another as well as track chemical changes in the atmosphere in general. This helps in understanding what happens to ash clouds which are ejected from volcanoes and even how chlorofluorocarbons, or CFCs (which were the major cause of the ozone hole) can impact the environment as a whole. This is operational science. A direct observation is made in well-defined conditions and then conclusions are drawn based on those specific conditions.

Making claims about the composition of the atmosphere on prebiotic Earth is much more difficult. We are unable to directly take measurements of the atmosphere at that point in history, and so instead, we must use secondary sources to help us make educated guesses at what the composition was like (i,e, looking at the composition of rocks in different layers or stages of history). Although the methods are still the same – we are still making observations (analyzing the rock layers) and then drawing conclusions from those observations, the conclusions that we draw have many more unknowns to them. No matter what the optimistic scientists claim, we can never truly know what the composition of early Earth was nor how life arose. Instead, we must just accept that although the historical science we are doing is good science, it will never give us an absolute answer.