There's no good way to do this. You can try running a short benchmark, but that may be affected by any other activity on the system. (E.g. if another app in the background did some work, it could drag down the performance numbers lower than they'd really be.)
Besides, there's tons of possible performance metrics. For example some systems may have high compute performance but low memory bandwidth, but others may have low compute performance but high memory bandwidth. If you run a performance test which is ultimately bottlenecked on memory bandwidth, but then your game actually does a lot of compute work, your performance benchmark result is not actually the right result. Software and hardware systems are incredibly complex with dozens of metrics and there's a huge array of configurations out there, so it's not really possible to come up with a single number.