Syncing Google Account on Galaxy S5 in preparation for transfer to a new phone

I finally got a new phone to replace my S5, but I've been trying forever (okay, about an hour) to sync my phone with Google Drive. It shows that some of the items, such as contacts and calendar, have synced, but a number of the other ones have the sync symbol next to them. I assume it's still syncing because if I go into the menu, I have the option to stop sync.

Is this normal or should I try to find a different way to sync my phone. This is the method recommended by my carrier. Do I need free space in order to sync?

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