How to use "WorksheetFunction.Match" as array with variable range

As you are using VBA, instead of using Match you could use the API to make for a more explicit and maintainable code:

Function FirstNonZeroCell(rng As Range) As Range
    Dim cell As Range
    For Each cell In rng.Cells
        If cell.Value <> 0 Then
            Set FirstNonZeroCell = cell
            Exit Function
        End If
    Next
End Function

Or if you want a more compact version (but less readable in my opinion):

Function FirstNonZeroCell(rng As Range) As Range
    For Each FirstNonZeroCell In rng.Cells
        If FirstNonZeroCell.Value <> 0 Then Exit Function
    Next
    Set FirstNonZeroCell = Nothing
End Function

Here is a sample of use:

Sub test()
    Dim res As Range
    Set res = FirstNonZeroCell(Range("A1:Z100"))
    If Not res Is Nothing Then
        MsgBox "Found value " & res.Value & " in cell " & res.Address & "."
    Else
        MsgBox "No match has been found!"
    End If
End Sub

Think the array element is throwing out your approach so here is an alternative.

It's not clear if you want the first non-zero value or its position so this covers both.

Date_col = Evaluate("MATCH(TRUE," & myRange.Address & "<>0,0)") 'returns position
Date_col = Evaluate("INDEX(" & myRange.Address & ",MATCH(TRUE," & myRange.Address & "<>0,0))") 'returns value

It's the first time I came across an "array formula" in VBA. This is not wrong, but not very evident to understand/troubleshoot. On my machine [where the range had all empty cells, it gives an error [myRange <> 0] = Error 2092, then within the Match function, then gets another error...

The array formulas are great in a formula worksheet only, but I feel you should avoid them in VBA. You have the ability to use loops in VBA, so, don't hesitate to use them! Having your train of though as explicit as possible is key when writing software (so you will understand it later!).

My suggestion would be this :

Option Explicit

Function FindDateColumnInRange(ByVal RangeToLookIn As Range) As Long

If RangeToLookIn.Rows.Count <> 1 Then
    'The range you're looking in has more than one row
    'what should you do in this case? Look only in the first row?

Else

    Dim i As Long
    'The range has only one row
    For i = 0 To RangeToLookIn.Columns.Count - 1
        If RangeToLookIn.Item(1, i).Value <> 0 Then
            'should you verifiy that the value is a date value?
            FindDateColumnInRange = RangeToLookIn.Item(1, i).Column
            Exit Function
        End If
    Next
End If

'the range didn't have a value different from 0
FindDateColumnInRange = 0

End Function

In action, you would get :

Sub Test()

Dim MyRange As Range
Set MyRange = Worksheets("Portf_Mod").Range("AB368:CY368")
Dim date_col As Integer

date_col = FindDateColumnInRange(MyRange)

If date_col = 0 Then
    'There was no date in your range
End If

End Sub

Yeah, it's a lot more long than SJR suggestions, but, it covers every exceptions and you can control how to look if you were to pass a multidimensionnal array (iterate through rows first then columns, or the other way around).

I wouldn't use the Match function for this...

Set myRange = Worksheets("Portf_Mod").Range("AB368:CY368") 
On Error Resume Next
Date_col = myRange.Find("*", LookIn:=xlValues, SearchOrder:=xlByColumns).Column
On Error GoTo 0