Proof is something like an equation or formula.
For examples, Einstein's famous mass-energy equivalence:
E = m c^2
That's equation is proof, not evidence.
Newton's universal gravitational equation:
F = G (m1 m2) / r^2
That's also proof, not evidence.
Ohm's Law:
I = V / R
Again, another proof, not evidence.
Equations and formulas are bunch of variables, some numbers; they are something that scientists have formulated, and it is part of formulation of the explanatory models.
Each of these equations can be right or wrong, and they are only valid if the evidence support the proof.
Evidence is carrying out testings in the field, discovering evidence, performing experiments to test a hypothesis, recording observation on video, taking measuring, and so on.
Don't get me wrong, Amanaki, mathematical proof is and can be very useful tools to science that allow scientists to frame their hypothesis in logical ways, but in the real world, maths and mathematical proofs don't always provide the correct solutions in understanding natural phenomena. That is evidence is far more important than proof.