Delay Autoresponder CF7

We have set up an automatic autoresponder based on a field input by adding an additional function. However, now it sends directly. What we would like is to send only that autoresponder after a delay, so the form itself may be send immediately.

I tried doing that by adding sleep() into the function, but then the person filling the form will also see the loading animation till that time is collapsed.

Current code:

//Autoresponder CF7
add_action( 'wpcf7_mail_sent', 'contact_form_autoresponders' );

function contact_form_autoresponders( $contact_form ) {
    // The contact form ID.
    if ( 47507 === $contact_form->id ) {
        $submission  = WPCF7_Submission::get_instance();
        $posted_data = $submission->get_posted_data();
        // Dropdowns are stored as arrays.
        if ( isset( $posted_data['location'] ) ) {
            switch ( $posted_data['location'][0] ) {
                case 'California':
                    $msg = 'California email body goes here';
                    break;
                case 'Texas':
                    $msg = 'Texas email body goes here';
                    break;
                default:
                    $msg = 'Unfortunately, that location is not available';
            }
            // mail it to them using wp_mail.
            wp_mail( $posted_data['your-email'], 'Thanks for your enquiry', $msg );
        }
    }
}

How can I add a delay to the autoresponder and still have the confirmation of the filled in form show immediately for the person that fills it in.

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