Here's the RE to grab what appears to be a date in your Caption field.
Regex([Caption], /#((?:Jan|Feb|Mar|Apr|May|Jun|Jul|Aug|Sep|Oct|Nov|Dec)\S*\s\d{1,2},\s*\d{4})#/, 1)
You can create an expression column to see that it works for you.
This grabs the date into one sequence. To format the date, we can't use this sequence directly, since you want to convert from month names into numbers, and MC's FormatDate() function uses internal date representations, not strings. So, we can assign the string to a new date field, where MC does understand and convert human-readable date forms, and then you can use that value inside FormatDate().
Create a new field, of type Date, lets call it "Date (Caption)".
Select your files, and use the RE above to pull the value from Caption, and place it into [Date (Caption)]. In the Tag Action Widow, or a column, select-to-edit the Date (Caption) field and enter the assignment expression:
=Regex([Caption], /#((?:Jan|Feb|Mar|Apr|May|Jun|Jul|Aug|Sep|Oct|Nov|Dec)\S*\s\d{1,2},\s*\d{4})#/, 1)
Now, you can use the expression:
formatdate([Date (Caption),0], yyyy-MM-dd)
wherever you want.