If you work in the US you should be getting a W2 from Google in a month or two. The top left corner will contain your SSN or it's an invalid W2 because the IRS won't be able to verify this is your W2 when you submit it with your tax return.
Yes, as I said from the other comment, I provided that when I started. From GP's comment, I thought they are saying they had to provide the SSN before they started.
