Or more broadly when did people start marking everything against a common level? Or say when was it known how many feet Rome was above the sea, or if New Delhi or Chengdu was higher?
You probably mean MSL, which is Mean Sea Level. In order to calculate the predicted height of a tide we work with amplitudes relative to a mean level as the tide approximates a sinusoidal behaviour. It was therefore necessary to measure the level of the sea surface relative to some arbitrary reference level, called Chart Datum (C.D.). As the tides vary in behaviour and amplitude throughout the world the MSL varies from place to place. By observing and recording the tidal heights over long periods of time it is possible to derive the height of MSL relative to this C.D. Unfortunately weather patterns like wind and atmospheric pressure influence tides as well, which also influences MSL and in various locations around the world the Tide Tables will indicate the variation in MSL during a year. As the need for this info arose with the advent of needing navigation charts it probably started in the early 1600's. I don't know whether the Romans were even interested in knowing how high Rome was above MSL.
My longish answer to the original question tells you how we go about establishing mean sea level, so I don't understand your additional question. If you want to know where this mean sea level is in your location get a tide table that has tidal info for your location and it will tell you where MSL is in your location. If your location is not contained in a Tide Table, get a chart for your area as it will also provide info on the reference level, i.e. Chart Datum, and the variation between various long term tidal heights, such as spring and neap high and low water levels so you can work out where MSL is. If you are lucky it may provide data on where the bench mark is in relation to chart datum so you could run a line of levels from it to the water's edge to see where that level is relative to CD at the time you do this. If you need more info buy a book on tides or navigation or ask a local harbour pilot or lecturer at a maritime college. I could recommend some books, but as I do not know anything about your skills in mathematics these could possibly be beyond your ability to cope with. As it is not efficient to keep on dealing through Stack Exchange you could contact me directly at email@example.com