: No one has proposed an alternate theory of how the universe began that fits
: all observed facts, like the recession of other galaxies, the
: omni-directional microwave background temperature, the wall of plasma
: beyond which nothing can be observed (the big bang glow itself), etc.
: That;s why the Big Bang Theory is still top dog of explanations. Sure
: something could oust it, but it would have to be something that still
: explains all observations.

This is precisely what I'm saying.
It's not observed, but it is the leading theory amongst many scientists that explains observations while taking those observations and extending them into the distant past, or through vast distances. This is the framework within which the Big Bang Theory remains the most viable explanation of observed phenomena.

: 'Observation' is not limited to what human eyes can discern in the visible
: portion of the EM spectrum. I not saying that's what you're implying, but
: it sounded similar.

"Experience" would be a more apt terminology. In science, experimentation and observation of the results (using whatever senses are required to 'experience' the result).

: Looking farther out into space is exactly like looking back in time.

But it's not. It's only an analogy based on assumptions about untestable properties of the light's path (eg, the source of the light, the light's own properties through its lifetime in the past, and properties of the space between the source and destination). Assuming the light's properties have remained constant, that it has not interacted with any other phenomena we haven't yet detected, and the laws of physics as we know them applied constantly throughout its travel, then we can mathematically predict the location or distance of the its source. Assuming the location is accurate to whatever degree we are capable of calculating, and applying the properties we have observed of light (specifically its measured speed here), we can predict the most likely distance to its source, and by extension how long it would have been traveling given those conditions. We can't prove it, as we can't travel there to test the prediction, but until any other discoveries somehow imply that our calculations are faulty, it's the best explanation for our observations.

We aren't looking back in time, we consider that we are looking at the light that has, as calculated above, been traveling for X amount of time, and so we consider the image we see as effectively what existed that amount of time in the past. Saying we're looking back in time when looking at starlight is like saying we're looking back in time when we look at a childhood photo that arrived in our mailbox.

: Looking at the sun right now is actually you seeing it as it
: appeared about 8 minutes ago. For the moon, about 2 seconds ago. For the
: nearest star to the sun, about 4 years in the past. We can't see anything
: in the 'present' when we look up into space.

Yes, what we are seeing is the state of light 'in the present', which as explained above, we presume has been traveling for a calculated amount of time. It is a snapshot of what we consider to be a state of the source of light X amount of time ago, based on the known properties of light. It's not looking into the past, it's looking at a snapshot of the past that exists here and now.

: It's probably close to impossible to create living matter from non-living
: chemicals in a world rife with life...too many instances to contaminate
: the experiment.

Also a non-answer, that it's impossible to demonstrate the point you're trying to defend. Scientists hate when people use that excuse :P.

: Finding life on another world (Mars, Europa, Titan, etc.)
: would do it for me, but only if it was not DNA-based life.

Right, that would be very intriguing. As it stands right now, it's stuff of science fiction, but the scientific efforts to seek out such life is certainly, in my books, a worthy mission.

: We already know
: rocks from Earth have could have reached Mars and rocks from Mars have
: definitely reached Earth through natural means, so even martian life could
: be contaminated by Earth. Or perhaps Earth life began on Mars and seeded
: Earth. Entirely possible.

Possible, but only posited at current time. You see how your belief that life "must have" come from non-life is painting your very opinions about what should be found if scientists look long and hard enough?
There's absolutely nothing wrong with that. But it demonstrates that we all start our exploration of the universe within some form of an axiom, some framework by which we interpret our observations as an attempt to strengthen the plausibility of what we're seeking to discover.
Nonetheless, finding biological life on another planet (presuming it can be determined that it wasn't contaminated by earth biology) still doesn't demonstrate that non-biological matter produced biological organisms with zero influence. It would still be a huge discovery, mind you, but it wouldn't solve that particular mystery.