I have seen this several times, but now I've tried to diagnose it. This is from an Azure WebApp. It shows a Purepath that seems to start only after some time, in this case one second:
Values vary from Purepath to Purepath, and sometimes they are negligible.
If we see the Code Level, it seems that the time is dependent on AcquireRequestState:
According to https://docs.microsoft.com/en-us/previous-versions/aspnet/bb470252(v=vs.100)
AcquireRequestState is still IIS before being passed to tha application. Checked other variables but have not been able to find anything that might explain this initial late start.