A simple module that'll tell you if your lambda is warm, by checking for the existence of /tmp/isLambdaWarm, which is the most reliable way to check this kind of thing (as the /tmp/ folder is shared across invocations).
If it's not, it writes the Date.now() when this module was invoked to /tmp/isLambdaWarm. That should give you an approximate time when the Lambda container was first booted.
const lambdaWarm = require('./index');
lambdaWarm(function (err, warm, date){
console.log(err); // any errors
console.log(warm); // boolean
console.log(date); // Date object with when this module was first ran in a lambda
});