There are warm and cold runs. If it’s really important you can pre-heat by calling the lambda every so often. It would be nice if they had some option for this.
There's Provisioned Concurrency for Lambda which keeps an amount of Lambdas warm at a price, so you don't have to keep pinging your function yourself to pre-heat.
This is news to me and exactly what I would have expected to exist. Good to know!
I suppose I can ping it upon page visit (for web apps). That never occurred to me until now.