Hi Bill,
Not to disparage your take on all things scientific, but when you say The Singularity, are you refering to the Big Bang? I haven't come across the term Singularity for it before, but have for other things (Black Holes, Human Singularity [evolving past biology, hmm, possibly too far to take this thread's already heady topic], and a couple of others).
But, just so we're clear, science is working on what came before the Big Bang. I've mentioned String Theory a couple of times, and it's expansion, M-Theory, proposed by Ed Witten. String Theory (and M-Theory) predict that there are at least 11 dimensions, the 4 most are familiar with (length, breadth, width, time), convex, concave, parallel, and so on. Most don't have names, refered to as the 9th Dimension, or the 11th, and so on. In this model, strings are on membranes, or branes, which are really nothing more than hugely stretched strings themselves. This allows for the "regular" strings (relating to electro-magnetic force, the strong and weak nuclear forces, matter, and others) to be attached to this brane, whereas the predicted gravitons (particles of gravity) are possibly disconnected, allowing them to move freely between dimensions, leaving the ones we are familiar with, and going into others, offering an explanation as to the ridiculously weak strength of gravity (as compared to the other forces).
But this theory goes further, proposing that the branes are actually rather frequent, and float through the multiverse, occasionally colliding with each other. And those collisions are what the Big Bang was, a collision of immense forces, releasing a fantastic amount of energy and matter.
But, of course, there are problems. For one thing, there is no way to test or prove any of this other than by mathematical equations to test whether or not it would stand up to known and established laws. Then you get the issue of not actually knowing what would happen if these branes did collide... it may result in a "Big Bang", it may not. If it does, then Big Bangs may be going on all the time, resulting in many Universes being created all around us, just out of our perception. And, of course, you will always have the question "yes, but what came before that?". But I thought you may like to know that science is certainly delving into what came before.
As for your oxygen example, you can test and see the results for yourself. You don't need to be a scientist. But in order for you to do that, you need to understand that "oxygen" is just a name used to describe a particular gaseous element with specific properties. Those include a certain number of protons, electrons (8 each) and neutrons (16), a certain atomic weight (16), and a place on the Periodic Table (8). But that is all very "science-y", and as you say, most won't see the elctrons and protons themselves. But what we can see is displays of it's properties that have an effect on the surroundings.
For example, one property of oxygen is that it burns, and burns quite nicely, thank you. To test yourself, try this
http://www.angelo.edu/faculty/kboudrea/demos/burning_splint/burning_splint.htm. It also allows us to breathe, by providing sustenance through our blood stream to the various parts of our bodies. Try not breathing (only for a short while, don't want to lose you!), and see the reaction of a lack of oxygen. Or check out the oxygen masks in a hospital, and see what happens when you remove them, or stop the flow... actually, probably best we don't do that one.
(Please note the above testing methods are by no means exhaustive, or entirely scientific [with removing oxygen masks etc], but are merely an indication to what can be done).
But, as you can see, even if you can't "see" oxygen itself, you can test for it's presence. I'll defer to Elder's statements about the operation of science here, as to improving existing models and providing new ones as evidence warrants, but realise that the Flat Earth Model was science until new evidence demonstrated a need for a new Model. And that is the way science continues today, constantly re-evaluating and re-testing, not leaving anything to faith, as it were.
Did you see NASA crash a rocket into the Lunar Pole? That was done to discover what it was made of. Now, there have been numerous missions to the moon before, and they have brought back Lunar materials, so you may say we already know. It's dry and dusty, and rather barren. But there is a theory that the poles may contain frozen water, so instead of just saying "No, we're scientists, we've been there and done that, and there isn't any", they re-tested and re-examined in a new way to possibly add to the model we have of the Lunar construction.