Things have been very quiet since the initial unofficial announcement, which was basically a gossip column post. There is no mention of this on the LCT website. Assuming this is the Sam Mendes production, and assuming they are going to use the cast from the most recent West End mounting that closed a couple months ago, they would probably only need a few weeks of rehearsal/tech in New York but if they are going to start performances at the end of September or beginning of October one would think that tickets would go on sale soon. There has been no casting notice posted for understudies, supernumeraries etc.
The production that recently played at the Huntington, which was an independent production, not the Sam Mendes production, was excellent, and made some very cool choices regarding acting and design.