Automatically translating from existing .po and .mo files?

Solved by adding

if ( isset( $_POST['language'] ) ) { // Input var okay.

    add_filter( 'locale', 'mbd_set_my_locale' );
    /**
     * Set locale based on the $_POST choice.
     *
     * @param  string $locale Locale code.
     * @return string         Selected locale code.
     */
    function mbd_set_my_locale( $locale  ) {
        $language = sanitize_text_field( wp_unslash( $_POST['language'] ) ); // Input var okay.

        if ( 'hr' === $language ) {
            $locale="hr";
        } else {
            $locale="en";
        }
        return $locale;
    }
}

Before initializing the main plugin class.