How can I determine whether a value exists anywhere within a multidimensional array variable with multiple levels?

I am trying to write a loop that adds various numbers to a two-dimensional array. The loop needs to check whether, for each loop case, a value associated with this case is already present in the array (and if it is, then skip to the next case).

If I have a single dimension array, I can use the MATCH function to achieve this checking task: 

Sub arrayfindtest()
    Dim data()
    Dim output As Variant
    
    ReDim data(1, 3)
    
    data(1, 1) = 1
    data(1, 2) = 10
    data(1, 3) = 3
    
    output = WorksheetFunction.Match(1, data, 0)
    Debug.Print output  
End Sub
However, if I add another level to the first dimension of the array variable, this doesn't work (as MATCH obviously only searches in one column). So, this doesn't work:

Sub arrayfindtest()
    Dim data()
    Dim output As Variant
    
    ReDim data(2, 3)
    
    data(1, 1) = 1
    data(1, 2) = 10
    data(1, 3) = 3
    
    output = WorksheetFunction.Match(1, data, 0)
    Debug.Print output
End Sub
In my scenario, two types of solutions would work: either a solution that checks whether the value exists anywhere in the array variable, or a solution where I specify one particular dimension of the array variable, and check in that.

Any suggestions much appreciated.