How soon can I list a house for rent?

[Dave Smith]

I went under contract for my first investment property yesterday. Closing date is 4 weeks away. It's a turnkey, single-family house, built in 2005 and doesn't need any improvements or fixes that I know of (pending home inspection of course). I'd like to have a tenant move in as early as possible. Obviously tenants can't move in until after closing, nor would I sign a lease until after closing. But how soon can I list it as available for rent and start screening lease applications? Do I need to wait until after closing to list it? If the contract falls through for some reason, and I have already listed it, what are the negative repercussions?