Usually no more than 20 to 30 days after listing, from what I've seen with friends' books and my own. So if there is no Amazon sales rank, that version is either not selling or is not offered on Amazon.
You can check versions to see if the book is out of print, or offered through third party sellers. Check the publication date, too. If there is no Amazon rank on a book over a year old, that's seriously bad news. Amazon isn't the only game around, but it is one of the biggest.
Don't go insane trying to figure out Amazon's rank-to-actual-sales ratio. One of the closest third party services is
www.salesrankexpress.com. And even they admit their numbers are not accurate at high sales volumes. Even at relatively low ones: my January sales via Amazon were listed as 55 through SalesRankExpress, but were actually more than twice that.
The service can seem eerily accurate when tracking extremely low sales (single digit sales per year). I had the opportunity to recently check this against both Nielsen BookScan and someone's royalty statement. In that instance, SalesRankExpress got it right: 8 copies sold through Amazon in 2013.