Filter out old posts site-wide

This is probably more of a WordPress question but I was hoping that someone here might be able to help me.
I need to filter out all posts that have a post_date of less than 1/1/2016. I am hoping there is a filter I can add to functions.php that will make the entire web site ignore all posts created before 1/1/2016. Or a plugin perhaps?

The problem I am trying solve with this is – we have a lot of accessibility issues in thousands of posts created before 2016 and rather than try to fix all those accessibility issues we want to simply make the site so that it acts as if they don’t exist without deleting them from the database.

Thanks!