Private Sub Worksheet_Change(ByVal Target As Range)
Const WS_RANGE As String = "B20"     '<== change to suit

   On Error GoTo ws_exit
   Application.EnableEvents = False

   With Target
       If Not Intersect(Target, Me.Range("A20")) Is Nothing Then
           If .Offset(0, 1).Value <> "" Then
               If .Value > .Offset(0, 1).Value Then
                   MsgBox "Invalid date"
                   .Value = ""
               End If
           End If
       ElseIf Not Intersect(Target, Me.Range("B20")) Is Nothing Then
           If .Value <> "" Then
               If .Value <= .Offset(0, -1).Value Then
                   MsgBox "Invalid date"
                   .Value = ""
               End If
           End If
       End If
   End With

ws_exit:
   Application.EnableEvents = True
End Sub

'This is worksheet event code, which means that it needs to be
'placed in the appropriate worksheet code module, not a standard
'code module. To do this, right-click on the sheet tab, select
'the View Code option from the menu, and paste the code in.

Select B20
Use Data | Validation, and select Date from the Allow options
Now in the Setting tab specify: Date: Greater Than" Start date A20
best wishes

You can either use the data/validation wizard to achieve this or
use vb to monitor this range

the wizard is easier