I also have this problem, and I can trace it back to having a native IPv6 internet access. When I disable the IPv6 protocol on my LAN interface, or move to a different network where the main connectivity is IPv4, Overwatch starts immediately.
I can reproduce this by disabling / enabling IPv6 e.g. using Powershell commands (as an Admin user):
Disable-NetAdapterBinding –InterfaceAlias “Ethernet 2” –ComponentID ms_tcpip6
Now Overwatch starts immediately …
Enable-NetAdapterBinding –InterfaceAlias “Ethernet 2” –ComponentID ms_tcpip6
… back to taking forever to start …