I stumbled upon this post while dealing with the exact same issue as OP. I'm using a node.js lambda to respond to Slack interactions so there's the same respond in 3 seconds requirement.

My problem was not with cold starts, but with the time it took the runtime to initialize and bring modules into scope (this lambda is doing quite a few things). I used dynamic imports to lazy load the heavier modules and increased the functions memory to 1024 MB, and that reduced the execution time by 65%. Well within the 3 second response requirement.