Impedance in RLC circuit
The impedance of an idealized RLC circuit does not change with time.  Your difficulty lies in the definition of "impedance", I think.

The impedance of a circuit at any given frequency describes how that circuit will operate in steady state.  Strictly speaking, "steady state" means how the circuit responds to a sinusoidal (or constant) waveform that has been the same forever into the past, and will be the same forever into the future.  Practically it just means how the circuit behaves after all the transients have settled out.