Question: How to define several tensor components in one?

Is there a way to define tensor components without addressing each component individually? Suppose I define a tensor A[a, mu], where Latin letters are space coordinates and Greek letters are space-time coordinates. Is there an easy way to define multiple components without having to define each component separately. For example, A[a,0] = 0 and A[a,i] = LeviCevita[a,i,j].

restart;
with(Physics);
Setup(spaceindices = lowercaselatin_ah)
g_[]
Define(A[a, mu])
A[a, 1] := 0
A[a, b] := LeviCivita[a, b, c]
TensorArray(A[a, mu]) 
A[1, 2] := 0
A[2, 3] := LeviCivita[2, 3, c]
TensorArray(A[a, mu])

The general writing method does not seem to change the tensor components, but the writing method in which I address the components individually does. What exactly am I doing wrong?