You have somehow become confused about what science is, because the definition you just gave to disqualify science is pretty much exactly what science is: "useful speculation". Science is a process. It begins with a question, moves then through speculation to a theorized solution to the question, and then to a series of tests designed to either verify of nullify the theory. This produces data that then leads the scientists to modify the question, and the proposed theoretical solution to the question, and on to another set of tests. And thus the process continues on forever.
The point is that science as a process doesn't "prove" anything. It's not even trying to prove anything. Scientists speculate, and then test those speculations to produce data. A scientific theory either "works" with the resulting data or it doesn't, and so must be modified and tested further.
In the case of the theory of evolution, it has been tested in many thousands of different ways over the last several hundred years by many thousands of scientists and has been modified and tested again and again and again, with the result that it "works" with a huge amount of accumulated data. It remains a theory, because that's all any scientific proposal ever is, but this particular scientific theory has been tested in many ways, by many scientists, over many years, and it "works" (meaning that it predicts accurate outcomes when tested) with the enormous amount of resulting data.
That's about as much "proof" as any human will ever have. So if it's still not enough for a person to reasonably accept, I have to suspect that they're being willfully biased against it.