First, why don’t you just export your spreadsheet as csv? Google has that feature built-in. It’s under the menu File > Download as > CSV
But, answering your question, it’s pretty easy to wrap all values in doubles quotes. Let’s say the desired values are on Sheet1 columns A to D. On Sheet2, cell A1, just place this formula:
=ArrayFormula(""""&Sheet1!A:D&"""")
The issue with the issue with the double quotes is that they’re used as string delimiters, so to have them inside a string you have to type two consecutive. So, one ” to open, two to have one “” and one ” to close 🙂