Which is where you find alternative outcomes from the same or similar processes, so you can compare the results to see if they corroborate each other. Like multiple independent methods of radiometric dating sitting on different decay chains, dating on different types of rock, cross-referencing between tree-rings and radiometric dating, etc. etc.
You can also go and do the tests in many different locations on similar types of rocks.
Neither is the present. You can’t travel 3 minutes back in time and re-do the exact same measurement. The world has changed since you did it, and you’re not really going to be doing the exact same thing again, by the literal meaning of exact. All your results, all your observations are always going to be inferential in nature. You’re going to be comparing things that you know, unavoidably, did not occur under the exact same circumstances.
What if I don’t have that luxury, how long do I keep going? At some point I have to stop and actually use the pipette in an experiment, someone is paying me to get stuff done. In the real world I will always, and only ever be in some constrained circumstance where I’m forced to work with the results and instruments I have within the reasonably allotted time. So now I’ll have to do statistics, and put error bars on stuff.
But then we’re back at square one, with no serious distinction between “historical” and “observational” science. We have a limited set of measurements that we can compare to models, and do statistics on and interpret.