Can I change a post's publish date?

Yes.

1. Open the post, and in its settings click the Date.
2. Pick the new date under Published on, and click Save date.
3. Deploy.

The date shown on the post changes, and so does its place in your blog's feed, which is ordered newest first.

To change the date of many posts at once, use Change date in bulk edit. To publish a post in the future, schedule it instead.