If you want to avoid the use of the SendKeys method, you could use the UIAutomationClient library or the SendMessage function from user32.dll. These would allow you to use the Windows API to interact with the dialog window.
There is not a lot of online resources on the UIAutomationClient library in VBA, but this video (and part 2) should be good enough to get you started.
EDIT:
However, if you decide to use SendMessage, here's an example of how to implement it:
1) Put the following at the top of the code module
Option Explicit
Private Declare PtrSafe Function FindWindow Lib "user32" Alias "FindWindowA" (ByVal lpClassName As String, ByVal lpWindowName As String) As LongPtr
Private Declare PtrSafe Function SendMessage Lib "user32" Alias "SendMessageA" (ByVal hwnd As LongPtr, ByVal wMsg As Long, ByVal wParam As LongPtr, ByVal lParam As String) As LongPtr
Private Declare PtrSafe Function FindWindowEx Lib "user32" Alias "FindWindowExA" (ByVal hWnd1 As LongPtr, ByVal hWnd2 As LongPtr, ByVal lpsz1 As String, ByVal lpsz2 As String) As LongPtr
Private Const BM_CLICK = &HF5
Private Const WM_SETTEXT = &HC
2) Add the following sub procedure and change the value of FileName to the desired value
Sub FillFileNameAndPressOpenButton()
Dim FileName As Variant
FileName = "(423)" 'Change this to the appropriate file name
Dim WindowCaption As String
WindowCaption = "Open"
Dim OpenDialogHandle As LongPtr
OpenDialogHandle = FindWindow(vbNullString, WindowCaption)
If OpenDialogHandle = 0 Then
MsgBox "Couldn't find the Window"
Exit Sub
End If
Dim TextBoxHandle As LongPtr, tempHandle As LongPtr
tempHandle = FindWindowEx(OpenDialogHandle, 0, "ComboBoxEx32", vbNullString)
tempHandle = FindWindowEx(tempHandle, 0, "ComboBox", vbNullString)
TextBoxHandle = FindWindowEx(tempHandle, 0, "Edit", vbNullString)
If TextBoxHandle = 0 Then
MsgBox "Couldn't find the textbox"
Exit Sub
End If
Dim Rslt As LongPtr
Rslt = SendMessage(TextBoxHandle, WM_SETTEXT, 0, FileName)
DoEvents
Dim ButtonHandle As LongPtr, ButtonCaption As String
ButtonCaption = "&Open"
ButtonHandle = FindWindowEx(OpenDialogHandle, 0, "Button", ButtonCaption)
If ButtonHandle = 0 Then
MsgBox " Couldn't find the button"
Exit Sub
End If
Rslt = SendMessage(ButtonHandle, BM_CLICK, 0, 0)
DoEvents
End Sub