WordPress change publish date with custom field

I have a WordPress news site.

The posts/stories have a custom date field to add a date for when the post was added.

The posts are stored in WP in the ordered they were added which could be different from the date that is added to the post in my news site.

The posts on the site are shown in date order using the custom field date.

Is it possible to update the Published date in WP and so update the order of the posts in WP based on the values in a custom field.

Its possible to open a post and edit the published on data but can this be done automatically using the custom field date.

I want to do this because the difference in order in WP backend and that on the site doesn’t work with next, prev posts so I thought if I could update the order in WP it would solive that problem.