Not to be dismissive, but the chances of that happening are almost non-existent. Even if the chips were coming out of fab right now and there was a board design that was vetted I would be surprised if AMC could get a 1PH mine running by the end of Q2. You're talking about a 2MW datacenter there, probably 3MW with cooling. That's going to be a massive facility and even the capital infrastructure outside the mining hardware doesn't spring up overnight.
Just look at how long it took the 100GH/s mine to ramp up to 500GH/s, and that's with the Bitfury design which is pulling about half the power per GH/s that this 55nm design will if it hits its specs. They started getting hardware online at the end of July/start of August, and hit 500GH/s at the end of the year.
I'm currently employed by a company who has multiple data centers around the world, one of which I am in charge of maintaining. I am fully aware of the logistics involved in getting a data center setup and it is far from the biggest obstacle here.
I do agree that the ramp-up time will be a significant factor, but to say that the possibility is "almost non-existent" is exactly what you claimed to not be, dismissive. Ken knows how to do calculations and there are plenty of DCs that would love to take on the recurring revenue that an operation like this would bring in. This is not some magical and mysterious process. It has been done before ActM and will be done after.
It's hard to look at the example of this "100gh/s" mine ramping up to 500gh/s because there are far too many variables involved in any one company's ramp up time. They may have hangups that ActM does not and ActM may have some that they did not. The only thing we can really look at is our available resources and timelines, which only Ken has on hand. He has been very tight lipped about the mining operation until now so I believe he has enough data available to put forth a reasonable timeline.
The chips are not even scheduled to be available until Q2. I don't think it's dismissive at all to say the chance of having 1PH/s online in Q2 is almost non-existent. Even if the chips arrive at the very start of Q2, you're talking about doing chip bringup, board bringup, volume production and installation in the span of a couple months. Like I said, I'd be surprised if they could get a 1PH/s mine done by the end of Q2 if the chips were just rolling off the line now. An end of Q2 timeline for having that hashing power online given the information Ken has let out on chip timelines is fantastical.
I'm unsure of cost, as that's not my side of the responsibility, but no, it absolutely will not fit in a garage.

When I say DC, I mean DC and a garage does not qualify. Ken is not going to build this DC, from the ground up, by June. Let's not be ridiculous. There are many, many enterprise-grade DCs that will rent you rack space and power. I'd wager that Ken is already in talks with a couple.
Edit: To lend a little more insight into why a Mining DC isn't that big of a deal I'll share this. One of our Computer Scientist's used to work for a major university. They rented rack space for some massive GPU farm that did all manner of medical science computations from the same DC we use. The machines ran 24/7 with multiple GPUs per server crunching away relentlessly and the DC didn't bat an eye at their power/cooling requirements. This type of thing has been going on since before Bitcoin.
Out of curiosity, what is the power budget for the DC you manage, and would you be able to add 2MW of hardware and say 200 racks (at 10kW per rack) without bumping out existing clients?
The type of Data Center I use and am responsible for is not a rental space. It is for my company, exclusively. We do use one about 40 miles away that does have rackspace for rent that could absolutely absorb 2MW (they're currently expanding into a one million square foot renovation). Off the top of my head the one "room" (it's more like a hallway with hallways off of it) we have at the commercial space holds ten rows with 9 racks per row so that's 90 racks in one "room" if you're using both sides of the area.