You could use the kickplate but there are a bunch of screw holes that would look aout of place for sure. You could get black brake sheets and have it sheared as well. However you will most likely never get the blacks to match without having the metal custom painted.

How wide is the exposed concrete vs the width of the flooring? I think it would make a transition out of flooring and glue it down to the concrete

get a piece of white oak and stain it to match the floor color.

run the trim all the way around the window (on the inside) Or, get some othe leftover flooring planks, cut it to fit inside the window, and trim it out.

I did it around my skylight. got the wood, stained it myself and installed it. I used some of the flooring planks and then used the 1X1 for the trim on the outer side

I also did the inside of this casement window w/walnut

and this garden window w/a type of teak

It's pretty easy to do. you could do any of the wood ideas, or get a paintable wood and paint the inside of it black

You can install a black marble threshold.

I almost feel like it would be more complete if the piece along the bottom matched the Walls in color and depth, it would make a complete square.

If you want to do match to the floor I would see if they could make it a lot thinner than 3/4" and route out the bottom to fit over the concrete and ease the top front edge:

Palimpset that’s what I was thinking but I would make it from the floor (assuming it’s wide enough). Just miter the front to hide the plywood edge.

I almost feel like it would be more complete if the piece along the bottom matched the Walls in color and depth

That's what I was going to suggest too.

Larger image.

I drew what I would consider

I'd cut a piece of white PVC baseboard molding to fit, attach it to the gap between the window and the flooring, and caulk around it. I assume you're going for modern, drywall returns so I certainly would not attach any casing around the top or sides of the window.

The obvious solution is to create a miniature reenactment of the landing at the beaches of Normandy using toy plastic army men on the thin strip of fake sand (concrete).

Defintiely! Any tips for keeping the sand clean?

"Any tips for keeping the sand clean?"

No, war is hell.

Where is the thermal break here?

"Where is the thermal break here?"

The window appears to be dual-pane with an aluminum spacer and probably filled with argon gas.

Yep. Like wearing a parka with running shorts and barefoot. Gonna be a temperature gradient. Fancy windows do zero good when sitting right on that thermal bridge from inside to outside. Condensation and temperature transfer are inevitable.