In rough order of effort-to-payoff:

1. Shrink the bundle. Cold start scales with how much code has to be loaded and parsed. Bundle with esbuild, tree-shake, and stop importing the entire AWS SDK when you need one client.
2. Move work out of the handler. Anything at module scope runs once per container, not once per invocation — put client construction there.
3. Do not open a VPC connection you don't need. VPC-attached Lambdas used to be the worst offender; it is much better now, but still non-zero.
4. Provisioned concurrency, only after the above. It works, and you pay for it whether or not traffic arrives.

Rewriting in Go is real but it is the largest change for a gain you may not need once the bundle is 2MB instead of 40MB.

Check whether the p99 is cold starts at all before optimising — AWS/Lambda publishes InitDuration separately. I spent a week on bundle size once when the real cause was a downstream database connection timing out.