The first page header will exist, even if empty, provided the different first page option is applied to the current section. I suspect what you want is to ensure the first page header has no content. In that case simply deleting the content of the header will achieve the aim of having an empty header e.g. as follows. I have added optional code to show if the header is empty.
Code:
Sub ClearHeader()
Dim secTemp As Section
Dim sectionNum As Integer
Dim oHeader As HeaderFooter
sectionNum = Selection.Information(wdActiveEndSectionNumber)
Set secTemp = ActiveDocument.Sections(sectionNum)
If secTemp.Headers(wdHeaderFooterFirstPage).Exists = True Then
Set oHeader = secTemp.Headers(wdHeaderFooterFirstPage)
If Len(oHeader.Range) > 1 Then 'Optional
oHeader.Range.Delete
Else 'optional
MsgBox "Header is empty" 'optional
End If 'Optional
End If
End Sub