When is it OK to start advertising a rental?

Hi BP! 

I'm in the final stretch of purchasing a duplex. My conventional loan should close on May 31st.  I have insurance and all the paperwork ready to go. I suppose anything could happen between now and then, but it feels pretty solid. My credit is excellent, income is top tier, debt is very low, and it would be my first property. Knocking on wood now.

The duplex is pretty much ready to rent as-is. The make-ready will take most of a day to complete and I'm planning to that the day after we close.

So, knowing all that, at what point do you think it'd be appropriate to ask the seller if he's OK with us advertising the rentals and tentatively scheduling showings for June 1?  Should I wait till close?  Or would it be prudent to have renters already lined up to see it on day 1?