Magento2 how to get quote order id

in my authorization request builder as apart of my payment method facade, I need to fetch the quote or order id to pass it to the client….

class AuthorizationRequestBuilder implements BuilderInterface
{
    public function build($buildSubject)
    {
        // get order here (type of order is MagentoPaymentGatewayDataOrderOrderAdapter)
        // this order doesn't have an id as its not placed yet
        $order = $buildSubject['payment']->getOrder();
        // how to get the quote id or the reserved order id?
        $quote = null; // <- how to get this?
    }
}