Uncheck the box “Send User Notification” by default on new-user.php

There does not seem to be an easy overwrite without replicating the whole user interface. So the quickest solution might be to un-check the checkbox via JavaScript:

add_action('admin_footer', 'uncheck_send_user_notification');
function uncheck_send_user_notification() {
    $currentScreen = get_current_screen();
    if ('user' === $currentScreen->id) {
        echo '<script type="text/javascript">document.getElementById("send_user_notification").checked = false;</script>';
    }
}

The script is only injected on the user-new.php page (see $currentScreen->id), then selects the checkbox (see document.getElementById) and sets checked to false.

Update: Instead of checking for the current screen in the function there is the admin_footer-{$hook_suffix} action that only runs on specific admin pages:

add_action('admin_footer-user-new.php', 'uncheck_send_user_notification');
function uncheck_send_user_notification() {
    echo '<script type="text/javascript">document.getElementById("send_user_notification").checked = false;</script>';
}