You're mistaken. Science doesn't ask you to take anything on faith. And it does not rely on 'proof', which is strictly for mathematics and is a concept which does not apply to the real world. That's a red herring offered up by the religious, and you've taken the bait. Science relies on evidence and on reasoning. 'Evidence' and 'facts' are not 'proof', and 'reason' is not 'faith'.

But you say it anyway. And then you proceed to refute yourself:

I believe that matter is composed of atoms (at one level of complexity) and those atoms are comprised of subatomic particles. I've never seen one, but I accept the chains of experiment and reasoning that postulate their existence.

Which is only reasonable. And you go further:

I teach science in a museum. I believe the scientific method is the best way we have contrived to try and discover how the natural world works with a minimum of interference from our preconcieved ideas. But the best scientist that ever lived (whoever he/she is/was) can never achieve perfect objectivity. That's why we publish, so others can repeat the experiment and compare the results.

All very true. But then you let yourself fall into this trap:

But for the non-scientist, even the well educated, there is a lot of scientific principle that has to be taken on trust.

Not so. You don't have to take anything on trust. That is what religion does, and science is not religion. You're perfectly entitled to review the evidence and the reasoning and disagree with it on the basis of other evidence and other reasoning.

You're also entitled to reject the findings of science out of hand for any reason or no reason. But that would not be reasonable, and therefore you would then find yourself outside the realm of science.

I heard a professor of history speculate once that all living creatures may be an expression of the spiritual plane into the material world.

I'll bet this professor didn't bother to explain the characteristics of this 'spiritual plane', but presumed that you would take the existence of such a thing completely on faith. Do you suppose that would be a wise course?

In any case, any person, deist or atheist, who professes to know The Only Truth is a dangerous dogmatic who should be viewed with suspicion and alarm by the rest of us.

The 'Only Truth', as you say, is a religious concept, and can only apply to religion, and not science.

You really need to be more careful about that fuzzy thinking if you're going to successfully avoid these traps. And nobody can do it for you.

No atheist is saying they can prove gods don't exist

You've also taken the bait, and you've also fallen into the trap of supposing there is such a thing a 'proof' in the empirical world. There is not. The concept of 'proof' simply does not apply. Instead, science relies on 'conclusions'. 'Proof' is a concept which properly applies only to mathematics. Popular language abuses these concepts, but in science these words have more precise meanings so as to avoid misunderstanding:

Moreover, "fact" does not mean "absolute certainty." The final proofs of logic and mathematics flow deductively from stated premises and achieve certainty only because they are not about the empirical world.

In science, "fact" can only mean "confirmed to such a degree that it would be perverse to withhold provisional assent." I suppose that apples might start to rise tomorrow, but the possibility does not merit equal time in physics classrooms.

Facts and theories are different things, not rungs in a hierarchy of increasing certainty. Facts are the world's data. Theories are structures of ideas that explain and interpret facts. Facts do not go away when scientists debate rival theories to explain them. Einstein's theory of gravitation replaced Newton's, but apples did not suspend themselves in mid-air, pending the outcome.

http://www.stephenjaygould.org/library/gould_fact-and-theory.html

Deities do not exist because there is no factual reasoning which admits of their existence. The Tooth Fairy and unicorns do not exist for the same reason. That's a 'conclusion', and not a 'proof'. And they are very different things.

If you'd like to accept that the imagination constitutes a different plane of reality, then you can suppose that deities exist - but only in the imagination, and not in the real world. Notice that the religious work very hard to confuse the real with the imagined, and do not want you to be able to make a clear distinction between them.

Try to be careful, particularly about semantic traps and the meanings of words.

It is literally impossible for most people to verify much about science, and certainly impossible for any one person to verify it all.

Which is rather beside the point. The point is that you can, if you want to and are able. In the meantime, you can suspend judgement on anything you like until you can verify it to your own satisfaction. No faith required. That's just another red herring.

It is not useful to hammer on technical definitions here.

Quite the contrary. If the meanings your words are indefinite, then your facts and reasoning will be that much more indefinite, and your conclusions will be that much more indefinite also.

Is it not so? And if not, why not?