Convergence is not the right terminology in Molecular Dynamics. You're typically waiting for the simulation to reach "equilibrium", or "steady state" if you are performing Non-Equilibrium Molecular Dynamics. The time to reach these states depends on the system studied and the property you're interested in. Some properties do not take long before the simulation reports a close-to-equilibrium value (i.e., pressure). Others (i.e., transport properties) take significantly longer.
As other's have stated, study the evolution of your target observables from two or more completely different initial systems, and how they converge to one average value (over some sampling time) to determine your relaxation/equilibration time. If they do not converge, your relaxation time may be significantly longer than you can calculate, or the system is prone to becoming trapped.
The time necessary for the observables to become independent from the initial configuration depends very much on the system and on the initial configuration.
For example, if you are close to the jamming transition, dynamic properties such as the mean-square displacement or the incoherent scattering function depend on the age t_a of the system. In this case, you would say the simulation "converged" when these observables become independent of t_a.
A different method that might or might not be applicable to your system is to prepare two "extreme" initial state and measure the time needed, until both systems become indistinguishable. For example, in an Ising model one could start with one state consisting of only up spins and one consisting of only down spins. The time needed for convergence would then be the time until both systems reach the same magnetization.
Convergence is not the right terminology in Molecular Dynamics. You're typically waiting for the simulation to reach "equilibrium", or "steady state" if you are performing Non-Equilibrium Molecular Dynamics. The time to reach these states depends on the system studied and the property you're interested in. Some properties do not take long before the simulation reports a close-to-equilibrium value (i.e., pressure). Others (i.e., transport properties) take significantly longer.
As other's have stated, study the evolution of your target observables from two or more completely different initial systems, and how they converge to one average value (over some sampling time) to determine your relaxation/equilibration time. If they do not converge, your relaxation time may be significantly longer than you can calculate, or the system is prone to becoming trapped.