Update the published date of a post to custom field date

I'm not sure if this is possible with WordPress or not. I googled a bit and didn't found any answers.

So I need to update the publish date of a custom post type with the custom field date I entered. This update should happen once the custom field date passes the current date.

That is if the custom field date is November 20, the post's publish date should update on November 21st and the updated publish date should be Nov 20.

Any ideas?