PostgreSQL - Date added row metadata
The only information you have about 'when' a row entered the table is the ID of the inserting transaction.  The sad news is that this is in no way connected to any real timestamp.

So you either add the new column (where you can't figure out when the existing rows were inserted) - or probably you can create triggers on all tables which populate a transaction ID-timestamp table.

The number of rows approach can work only if you keep track of not only the inserts but deletes (and truncates) as well.

Alternatively, if this task is not needed too often, you can use PostgreSQL's point-in-time recovery mechanism to set up a database which mirrors the state of a given time in the past, then compare the data in the two versions.