They don't. The $300 installation fee doesn't cover the cost of running fiber to your house + the cost of the box.
But it's hugely cheaper to wire your house at the same time they are wiring your neighbours. That's the catch -- the deal disappears once the neighbourhood is connected. They're not going to do a truck roll for $300.
Once your house is connected, upsell potential is a lot better than if it isn't.
It's laying the fiber that's the expensive part, and there is a $300 fee to pay for that. In terms of marginal cost, it really doesn't cost them anything to serve another 5MB/1MB connection. They want to get you hooked so you'll want to upgrade later.
They don't, but I'm guessing since they're just entering the industry having more subscribers is their number one priority right now. Delivering a product at a loss is nothing new.
First, they're hoping many of these users convert to gigabit after a short time ("Just flip the switch, and you get 200x faster internet!"), which will cover the loss from the free users.
Second, straight market penetration. The more people that use the service (even the free one), the more visibility Google gets as an ISP, which has other benefits.
Google has a private working relationship with the NSA - so its anyone's guess but it is conceivable that Google is receiving money from them to subsidize this cost.
