I have an Acer laptop with a 500GB spinning disk, and I started experiencing the same thing after upgrading to Windows 10.
I have shut down as many things as Win 10 Home will let me, such as file indexing, search, etc. But after boot I still see my disk usage go to 100% for a while after first booting up. Once I let it finish and settle down, everything works fine!
At this point the delay has been cut down from about 10 mins, to about 2-3 mins. Unless it has been a while, and everything starts automatically checking for updates at the same time. That will beat a 5400RPM drive to death as well.
What I usually see in task manager is that Windows processes are mainly behind this, particularly related to Service Host and
Superfetch. I could disable that like I did on my PC with an SSD, but it probably helps performance to leave it enabled on a spinning drive.
If I swapped the drive in my laptop to SSD this problem might go away, or at least become so quick that it wouldn't be detectable. Plus I would disable
Superfetch in that case. But unfortunately the drive swap on my laptop model is very difficult as it requires a near total teardown to access the drive. If you are lucky enough to have an drive access door in the bottom of the case, I would say go for the SSD!