Create buttons to scroll through timeline

Sure, just add a Global Variable and modify the procedure as follows.  That should do the trick.

Option Explicit
Public glblDate As Date

Sub Timeline_curr()

    Dim CurrentWeekDateOffset As Date:   Dim Csd As Date:  Dim Ced As Date
    Dim PreviousWeekDateOffset As Date:  Dim Psd As Date:  Dim Ped As Date
    Dim NextWeekDateOffset As Date:      Dim Nsd As Date:  Dim Ned As Date
  
    Select Case Application.Caller
        Case "shpCurrent":
            glblDate = Date
            CurrentWeekDateOffset = Date
            Csd = CurrentWeekDateOffset - Weekday(CurrentWeekDateOffset, 2) + 1
            Ced = CurrentWeekDateOffset - Weekday(CurrentWeekDateOffset) + 6
            ActiveWorkbook.SlicerCaches("NativeTimeline_Date").TimelineState.SetFilterDateRange Csd, Ced
        Case "shpPrevious":
            If IsNull(glblDate) Then
                PreviousWeekDateOffset = Date - 7
            Else
                PreviousWeekDateOffset = glblDate - 7
                glblDate = PreviousWeekDateOffset
            End If
            Psd = PreviousWeekDateOffset - Weekday(PreviousWeekDateOffset, 2) + 1
            Ped = PreviousWeekDateOffset - Weekday(PreviousWeekDateOffset) + 6
            ActiveWorkbook.SlicerCaches("NativeTimeline_Date").TimelineState.SetFilterDateRange Psd, Ped
        Case "shpNext":
            If IsNull(glblDate) Then
                  NextWeekDateOffset = Date - 7
            Else
                  NextWeekDateOffset = glblDate + 7
                  glblDate = NextWeekDateOffset
            End If
            Nsd = NextWeekDateOffset - Weekday(NextWeekDateOffset, 2) + 1
            Ned = NextWeekDateOffset - Weekday(NextWeekDateOffset) + 6
            ActiveWorkbook.SlicerCaches("NativeTimeline_Date").TimelineState.SetFilterDateRange Nsd, Ned
    End Select

End Sub