Mr David is correct: What your describing is a Slab leak. This is not a do it yourself type job. Its even a bit of a specialty for plumbers. meaning not all plumbers are experienced and competent in leak detection, those will ususaly call out a leak detection company to find the leak then they will do repairs/repipe/re-route.
You can't always rely on meter movment to prove the abscence of a leak especially the smaller leaks, Ive run across this several times. the sound is moving water. if you still hear it with a every possible leak or drip source accounted for, lightly or otherwise, a running toilet, dripping faucet, ice makers, R.O Systems,lawn sprinkler valves, hose bibbs all tightly holding. Then the next step is to call a pipe and leak detection service
(the Moen or Mixit cross over condition usually don't not make any sounds, only affects temperature)
We will verify the above then listen for the two loudest fixtures, the leak will be bewteen them on that loop (if copper)
(if Galvanized repairs can be done but I do not recommend it. move straight to a Full or partial repipe or reroute.
I would locate the manifolds for a reroute, For a conventional dig up repair I would locate the pipes then pinpoint locate the leak. Hot water gives one more tool to use, heat (digital thermometer) In order to hear the smaller leaks better we often administer pressurized Air Or C02 or helium to the piping system with water on and off to increase sounds and listen to it with and without water on, to help us hone in on the leak.
Depending on where the leak is will determine the cost involved and possibly the repair method best suited for this particular situation.
Depending on history of the home and neighborhood with regard to slab leaks it may be the best route to repipe everything up out of the ground as one leak may mean more. More than one slab leak almost always mean more down the road.
Repiping is always the best and ultimate answer for slab leaks, No more tearing up floors, it just costs more so most try to do the minimum.
but that is there gamble not the plumbers.