It is possible!
In settings.json which you can open via File>Preferences>UserSettings
UPDATE 2023
There are two settings
"editor.autoSurround": "never",
Possible values:
- “never”
- “languageDefined” – This is vsCode’s default
- “brackets” – meaning it automatically adds brackets, but not quotes
- “quotes” – meaning it automatically adds quotes but not brackets
"editor.autoClosingQuotes": "never",
Possible values:
- “never”
- “languageDefined” – This is vsCode’s default
- “beforeWhitespace”
- “always”
PS: In old ancient versions of vsCode, there was less granularity and a single setting would control quotes, braces and brackets. "editor.autoClosingBrackets" : "never"