Delay between a web hook and API response returning correct data

We want to get different conversation stats when we receive a onAdminAssigned web hook. Since the statistics object is empty in the web hook payload itself, we have to make a REST request to api/conversations/{id} to get a full conversation payload.

We noticed that if we make this call immediately after getting a web hook, the statistics object will still be filled with zeroes. But if we wait for a couple of seconds before making that call, then we can get all the data we need.

Could you pls provide an estimation of the delay (average and upper boundary) between a web hook being sent and the data being accessible via RES API?

Is it possible to send conversation statistics in the web hook itself?