In order to bring in data from Google Sheets the date has to be formatted in one of the accepted date formats provide by Google.
To view the accepted formats click "Format"-->"Number"-->"More Formats"-->"More dates and time formats..."
If you are unable to get your date format, that could mean it is a string. You can use =DATEVALUE to try and convert. Here is a support article from Google.
Quarterly data is not an actual "date" in the eyes of Google or many databases. You'll need to still format the quarter as a date.
Here is a quick tutorial video to give you a hand: