async function completeCheckout(orderId) {
  await updateAnalytics(orderId);
  const order = await processOrder(orderId);

  return order;
}

Because processOrder doesn’t depend on the result of updateAnalytics, you can parallelize the two invocations.

async function completeCheckout(orderId) {
  const [_, order] = await Promise.all([
    updateAnalytics(orderId),
    processOrder(orderId)
  ])

  return order;
}