It’s much more difficult to gain understanding for the very thing we are enmeshed in, using tools that only exist inside that thing.

Large Hadron Collidor go bzzzzzz

But it is true that the LHC does qualify as a tool which exists in the universe studying matter which makes up the said universe, by smashing pieces of it together and seeing what happens. However, while it is more difficult to understand the true nature of matter using tools made of matter, I am sure it is not impossible. Maybe we will find a way to overcome after we have gained the ability to manipulate the interactions between subatomic particles and solved the mystery of time. Who knows, but I have full faith in our descendants to kill god once and for all by overcoming the fundamental ignorance that we have towards reality which you outlined.

Not all things can be proved by the scientific method, nor should we strive to do so.

I partially agree since there is no use in proving shit with the scientific method when people are dying from hunger in a world full of resources. However, maybe in the future we can come up with another better system of thought which will unlock the secrets of our universe.