During the sync, propagate a new peer document and start listening to the network
We can listen to the network even if we don't have a blockchain: using WS2P private for example.
This way even if the sync takes a lot of time, we can keep up with the network's HEAD by receiving the new incoming blocks. Also, we would get notified of each node's HEAD packet and display a view of the network during the synchronization.
This could help the user to understand what is the final state to reach. For example we could say "the node will reach this consensus".