This should be possible using the Views Bulk Operations module (=VBO) ... Quote from its project page:
... augments Views by allowing bulk operations to be executed on the displayed rows. It does so by showing a checkbox in front of each node, and adding a select box containing operations that can be applied. Drupal Core or Rules actions can be used.
So create a view that lists all "content waiting to be published", whereas you might want to limit the access to such view to only that "one person" (the content approver?).
Then have the content approver use VBO to select "all" content to then apply "bulk operation" = "publish".
Should you want to do so, you could further enhance/refine this content approval process with modules Flag and Rules modules also. Refer to these questions to get an idea of the possibilities: