Excel or Google Sheets help

[CeeBee]

It's doable, but requires macros. I don't know how well GS can handle it. Many mobile editors seem to get stuck on macros.
Alternatively [ Ctrl ; ] is a nifty shortcut
Or https://yourbusiness.azcentral.com/i...cel-10658.html

But if you want the macro route...

Option Explicit

Private Sub Worksheet_SelectionChange(ByVal Target As Range)
    If Target.Cells.Count > 1 Then Exit Sub
    Dim lookupRange As String: lookupRange = "A1:A10000"
    Dim timeNow As Date
    If Not Intersect(Target, Range(lookupRange)) Is Nothing Then
        If Target(1, 1) = "" Then
            timeNow = DateTime.Now
            Target(1, 1).Value = Format(timeNow, "yyyy-MM-dd hh:mm:ss")
        End If
    End If
End Sub

Add the macro into the sheet...
It will only insert the date if the cell is empty.
I'd just leave the date/time as is and format the cells rather than modify the code to spit date OR time.
Change the cells range watching for click as needed...