I hope June 24 is not the only day you can visit. Do you want the house/museum only ticket (pretty easy to get) or the House + Introductory program ticket? (very hard to get). I've been "practicing" getting on the site at 5am CST almost every day and navigating around in anticipation of purchasing mine on April 15. I have been looking at the ticket + introductory program. They do not usually become live (white calendar square with a dark date, not gray) at exactly 12 noon Amsterdam time. Looks to me like they turn the house only tickets on first. Then the house + intro several minutes after. Anyway, a couple of weeks ago I kept checking over the course of several hours and the 60 days out Intro ticket date never came live. Later in the day it was completely pink. I emailed the museum and they said no programs were available that day (didn't give reason) so they did not activate that date but regular house only tickets were still available. After that, I noticed the 24th is already pinked out, so it looks like they marked it pink in advance so others would not be trying in vain all morning like I was.
And just a reminder- notify your credit card in advance so when you do get onto the site and get the tickets in your cart, your card will be accepted. If it is not, the cart will time out and you will need to start over and probably be out of luck getting one with the Intro. If you are only wanting the house and museum ticket (without the intro program) those are much easier to get. In fact, I just checked and as soon as May 13 plenty of those tickets are still available, but mostly in the evening.
Hope this helps. Good luck!