Hello,
This issue appears to be a question about your specific implementation rather than a problem with the product or library.
By default, in Dialogflow Essentials, webhook fulfillment has a response 5-second timeout limit (10 seconds for the Google Assistant integration) and this response must be at most 64 KiB in size.
If a webhook does not respond within 5 seconds, you will get this error: 'Webhook call failed. Error: DEADLINE_EXCEEDED'. So you will most likely have to optimize your webhook to prevent hitting the timeout limit.
1) It may be an issue in your code – you may be trying to trigger an intent that doesn't exist.
2) It may be a cold start (See this answer on another Groups thread)
3) It may be that your service calls other services/DBs, and those are slow to respond (this looks like the most likely possible root cause due to your use case).
4) Multiple parallel requests handling
But it could still be something else.
As workaround, you could use the CX edition where you can set up the timeout limit up to 30 seconds.
You could also, if you don't use any Dialogflow Essentials integrations, consider using only Dialogflow API, without using webhook. This approach may have its downsides, but it can also give you more control over your implementation.