I would not include the user field on the front end form at all, it would be a field that only the site admin could manage on the back end.
In the pre_save_post filter that you’ll be creating I would get the current user ID and then after adding the post I’d use update_field() https://www.advancedcustomfields.com/resources/update_field/ to update the user field. Make sure you use the field key when calling update_field() and not the field name for $selector.
