Hiya @jeffer
Posts always need to be assigned to an author. So what I’d suggest is create a user in your admin to whom these posts will be assigned – Anon User – or whatever you’d like to call them. Remember to make sure they’re of the correct role to publish posts.
Then in your acf_form
function, specify this user to be the author of that post. In the args for your form, just add 'post_author' => 123
– where 123 is the ID of the user you’ve created.