any measurement of the quantum system will collapse the system to the state which was the result of the measurement
This is correct, but irrelevant. It is possible to make entangled measurements (like, say, Bell state measurements) where all of the basis states are entangled, and the wavefunction collapse will send the system to an entangled state (and, just as importantly, tell you which entangled state you have).
More generally, what you're looking for is something called an entanglement witness: these are observables which, when measured can unambiguously certify that the states produced by a given preparation procedure are entangled.
That said, it's important to note that your conception of entanglement,
measuring one particle and then by the definition/concept of entanglement you will know the result of a measurement of the other particle
is blurry and ultimately inaccurate. Entanglement refers to a broad class of bipartite states that show correlations between measurement outcomes on the two systems (and which, moreover, can produce results for certain metrics of correlation that are impossible for classical systems), but the naive "if A is spin up then B is spin down" is too restrictive and fails to meaningfully demarcate the line between entanglement and classical correlations.
