You need to loop through the posts and update the field, yes you could do that.
get posts
while have posts
the post
update value
But I wouldn’t.
The best way to do this is to check the value where it is used and substitute a default value if it’s not set, it only takes a couple lines of code to deal with it.
$value = get_field('your-new-field');
if (!$value) {
$value = 'the default value';
}
// do something with value
you could also add an acf/load_value filter for the field in question that sets the default value if it is empty https://www.advancedcustomfields.com/resources/acf-load_value/
