Sorry, Hettie, but you can't provide positive proof of things. That is elementary philosophy of science. Evidence and proof are not the same thing
Evidence is the building blocks of proof. You arrive at proof by presenting evidence.
I cannot even begin to imagine where you got the idea that you can't provide positive proof of anything. If that was an elementary philosophy of science, science would be pointless.
You don't think it's been proved that hearts pump blood around the body? That chopping off a head will kill someone? That women provide eggs and men provide sperm? I think those things have been proved.
You are wrongly assuming that proof = 100% certainty. Only in maths does it mean that.
You're also assuming that proof is a thing. It's not. It's an argument using evidence to demonstrate the truth of something.
Empiricism does not imply solipsism. To say that it does shows a fundamental lack of understanding of what empiricism actually means.
That knowledge comes to us through our senses does NOT mean that it's meaningless unless we have personally experienced something for ourselves.
You can make that argument if you like, quoting Descartes & cogito ergo sum, etc.....but that is not empiricism, Niminy....that is not what it means.
When empiricism says that knowledge is acquired through sensory perception - it means the collective sensory perceptions of the entire human race.
We individually perceive things through our senses but we test those perceptions against the perceptions (which if tested may lead to evidence) provided by others.