'Looked at': No! There is no 'look history' like Edit or View (those have a 'Recent" under file, but not an auto-open on launch
You can configure how Calibre Sorts at startup: (so books added are shown recent to oldest)
Preferences: Tweaks"
Code:
ID: sort_columns_at_startup
Provide a set of columns to be sorted on when calibre starts. The argument is None if saved sort history is to be used otherwise it is a list of column,order pairs. Column is the lookup/search name, found using the tooltip for the column Order is 0 for ascending, 1 for descending. For example, set it to [('authors',0),('title',0)] to sort by title within authors.
You can Apply a VL at startup