Understanding the Requirement: The company wants to improve caching to enhance website performance while ensuring that stale content is not served for more than a few minutes after a deployment.

Analysis of Options:

Set CloudFront TTL: Setting a short TTL (e.g., 2 minutes) ensures that cached content is refreshed frequently, reducing the risk of serving stale content.

S3 Bucket TTL: This would not control the cache duration for the CloudFront distribution.

Cache-Control Private: This directive is for controlling caching by private caches (e.g., browsers) and is not applicable for CloudFront.

Lambda@Edge: While this can add headers dynamically, it adds complexity and operational overhead.

Cache-Control max-age and CloudFront Invalidation: Setting a longer max-age for objects ensures they are cached longer, reducing load on the origin. Invalidation ensures that updated content is refreshed immediately after deployment.

Best Combination of Caching Methods:

Set the CloudFront default TTL to 2 minutes: This balances caching and freshness of content.

Add a Cache-Control max-age directive of 24 hours and use CloudFront invalidation: This ensures efficient caching while providing a mechanism to clear outdated content immediately after a deployment.