For high-demand show, they will often increase the window. This is primarily to detect bots and people buying more than the maximum number of tickets.
Hamilton posts the shipping delay on the Ticketmaster page when you purchase. Usually a few months before the show, but also a few months after you buy them. Scalpers typically don't want to wait months before having inventory to sell, so this is a deterrent. And, if you are seeing the show, sort of irrelevant.
They are doing the same for Dolly now, I believe.
That said, if you have to travel to NYC, and have to leave before your ticket arrives, the box office can sort you out. So you'll be fine.