You can check "Preferences->Change Calibre behaviour->Advanced->Tweaks" a
window opens. Click on "Specify columns by which to sort the booklist on startup" and edit the tweak to:
Code:
# Specify columns by which to sort the booklist on startup
sort_columns_at_startup = [('date', 1)]
Then click "Apply changes to this tweak" and "Apply" in the upper-left corner. After restarting, Calibre should automatically display your library sorted by date. The 'date' in this case is the column, the 1 means descending while 0 means ascending. If you wanted to sort on a different column, e.g. a custom column of yours, you could change 'date' to '#mycustomcolumn'.
Unless you meant something completely different by auto-sort? You can simply click on the column headings for sorting to apply to the view.