Axios doesn't post on cold start

I have a function that is triggered when an SES email is received. It’s based on this serverless example:

I have added an extra step that uses Axios to post data to a webhook. The problem is that the post never happens on a cold start. I can trigger it again immediately after the first try and it completes successfully. There are no errors reported on the first run.

Any tips or gotchas with something like this?