At it's core, this URL shortener is just S3 redirect objects [0], behind a cloudfront CDN. So by "fast", you probably mean one of these things:
1) User clicking on a URL: the latency of this action is mostly determined by the latency of cloudfront, which is pretty fast [1]. (Except in the case of a first-click when cloudfront has to do a pull from S3, which is also not bad [1])
2) Creation of a new short URL: this action is the execution of a lambda function, which in my experience is ~1s in cold-start scenarios, and near instant otherwise.
1) User clicking on a URL: the latency of this action is mostly determined by the latency of cloudfront, which is pretty fast [1]. (Except in the case of a first-click when cloudfront has to do a pull from S3, which is also not bad [1])
2) Creation of a new short URL: this action is the execution of a lambda function, which in my experience is ~1s in cold-start scenarios, and near instant otherwise.
[0]: https://docs.aws.amazon.com/AmazonS3/latest/dev/how-to-page-...
[1]: https://www.quora.com/What-are-typical-latencies-for-static-...