No, this is not possible. This will happen in only very severe cases (think links to child porn) and often those are redacted and not hard-deleted.
By posting content on Stack Exchange, you've agreed to the Terms of Service which state the following:
You agree that any and all content, including without limitation any and all text, graphics, logos, tools, photographs, images, illustrations, software or source code, audio and video, animations, and product feedback (collectively, “Content”) that you provide to the public Network (collectively, “Subscriber Content”), is perpetually and irrevocably licensed to Stack Overflow on a worldwide, royalty-free, non-exclusive basis pursuant to Creative Commons licensing terms (CC BY-SA 4.0)
Requesting permanent deletion would go against that. You do have the option to request disassociation by the same license, but if it's just a couple of posts only a handful of users can see (and only if they're actively looking for them), why bother?