Haha, I hear ya on that.
Would a hammer drill do the trick?
I have done a lot of hammer drilling with a bosch bulldog and masonry bits. It would do the job with the right bit, but I would be concerned about breakout on the surface around the hole and getting the hole square would worry me, especially if using the hammer setting. If going that route I would want an opportunity to practice before trying it for real.
I once rented a hand held core drill so I could drill a 1.5” or 2” hole in my block basement and run electrical conduit to my garage for a sub panel. If I were doing this job, I would explore renting a pedestal mounted core drill and see if I could find a 5/8” bit for the rental.
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I drilled my plate as well. I used my floor mount drill press and stuck a block between the base and the bottom of the plate table so the drill press was acting like a “C-clamp Drill”. To @DEVLINCC ‘s point, it doesn’t have to be square. There just needs to be enough room for a square bolt to pass through it. The top and bottom of the plate will ensure the final post is square. Go slow, lots of water and time. I found some plumbers putty and built a dam that contained the water. If you forward from that image you can see the progression. You’ll get an inch or so down and then have to break off the core before you can continue. I suppose that depends on the type of cutter you’re using.
Untitled by Duane Draper, on Flickr
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As long as the hole is big enough for the bolt to pass through perpendicular to the top surface you’ll be ok. No shims.
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That’s a better way to say than I did! haha. A square bolt!! haha
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Haha. I didn’t even pick that up 
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Thanks all. Makes total sense. I’ll be drilling the hole here before too long. I think a 3/4” hole should work for my 1/2” requirement.
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