The questions that led the ancients to posit and underlying, self-existent, immaterial, unified source of Being were not scientific questions - though early on they were investigated as such.
They wanted to know how it was possible to have knowledge at all. What made a think itself, and not something else? How can we have knowledge of anything in a changing world?
These are basic problems of epistemology. Science doesn’t, can’t, and isn’t supposed to answer them. We can all see that in fact, we do seem to be able to discern things, come to conclusions, differentiate a rock from a tree, and a tree from a branch. But the question is, how?
You can deny philosophy reflects any reality, but you deny science then as well. If you want to say that the methods of science have reality, or reflect reality, then you can’t deny the principles it rests on, which are non-scientific principles. You want to have your cake and eat it too. Are you so attached to believing only what you can see and feel directly? If so, many of the methods of science should be lost to you as well - mathematics could be quite dodgy with that view. (In fact Plato thought that mathematics was the epitome of philosophy.) If you want to deny the possibility of any sure knowledge, you would be best off to follow Diogenes, who was at least consistent in his treatment of all knowledge.
My first remark concerns mathematics. Mathematics is
not science
in the strict sense. It is an asbtraction, which is based upon some selected axioms. We can agree to call it “
abstract science” along with “formal logic”, and as long as we are both aware of the distinction, we are on firm ground. The truths of mathematics are
contingent upon the axioms - which can be chosen arbitrarily. It is a major error to think about mathematical truths as “absolute”.
Second remark: The fact that you decided to bring up mathematics already shows to me that we are not on the same page. Mathematics says nothing about reality, though some mathematical constructs can be used as wonderful models of reality. I explictly said that the scientific method is only applicable to discern
truths pertaining to physical reality - and that implictly excludes mathematics and the other “abstract sciences”. I did not mention them explicitly, because I trusted you to see the significance of omission, and did not wish to waste our time to belabor the obvious. In the light of your post it was an error on my part. Sorry.
Third remark: you say that science cannot answer the question “how do we gain knowledge?”. In this question the “how” is ambiguous. If it asks: “what neural processes are involved in gaining knowledge about reality?” then this question is very much a sicentific question, belonging to biology and neurophysics - about which the “ancients” had absolutely no idea. If the “how” means, “how is it possible to gain knowledge about physical reality?” - then we use a few, basic, unprovable assumptions (and all basic assumptions are unprovable).
So, contrary to what you say, I do not accept “only” what I can see and touch. I know that science is also founded on a few basic, unprovable principles - among them is that the universe is “knowable”, the universe is “consistent”, that there are “laws of nature”. Now, contrary to what you imply, these basic principles did not come from some empty musings of some philosophers contemplating their belly-buttons in the seclusion of their ivory-towers. The are
distilled from innumerable observations of innumerable “experiments” by innumerable humans.
Fourth remark: “it all started with the senses”. Those ancients might have contemplated “how do we tell the difference between rock and a tree?”. The answer is “look at them, touch them, lick them, feel them…”. Use your senses. As before, there is
no a-priori argument that our senses correctly reflect reality. There is no need for such an argument. The only reason we trust our senses, is that they
work. The verification is a-posteriori. If someone would discard their own sensory (name removed by moderator)ut, they would die very quickly, and with their death their incorrect worldview would be “Darwin’d out”

.
Again, contrary what you
seem to believe: materialists / empiricists do not believe that “only the empirically verifyable propositions can be considered true”. (Unfortunately there are a few idiots on the board who keep on quacking this incorrect idea - no matter how many times their nose is rubbed into their excrement. Don’t be one of them.

) Propositions are considered true under 4 circumstances:
- if the are basic principles of physical reality (selected during innumerable observations),
- if they are some arbitrarily selected axioms for a formal system,
- if they correctly reflect the physical reality,
- if they are the logical corollary of a set of axioms.
Fifth remark: None of these cover the so-called supernatural realm. But as a materialist, I see no need for that hypothesis. All I wanted to show here that the materialist / empiricist stance is perfectly adequate in explaining itself and the physical reality.