Time is not special regarding symmetries and conserved quantities.
In general you can consider any family of continuous transformations parametrised by some real variable s: be it translations by a distance x, rotations by an angle φ, etc. These are technically one-parameter subgroups of a Lie group.
Then, if your dynamical system is symmetrical under these transformations you can construct a quantity whose derivative wrt s is zero.
Then, if your dynamical system is symmetrical under these transformations you can construct a quantity whose derivative wrt s is zero.