Text to date field conversion

in QGIS I created a point layer with a field which was initially set as text. For each feature, I wrote in that field a date: "yy.mm.dd". I then modified the field to "date" with a format yyyy-mm-dd.

Now, all the features created after the type change have the date in the new format and stored as dates, while features created before the type change have date = NULL. Actually, in the column preview of the attribute table I can see the old text stored in the field, so I think the original information is stored, despite in the "wrong" format.

Is there an automatic method to retrieve the old dates and store them as dates with the new format?