Expected behavior
Normally, when you have the taskbar at the top of the screen, Windows will not open a new program window in such a way that the titlebar is placed underneath and obscured by the taskbar. This is not possible, even if you forcefully try to do this.
Here I have the taskbar at the top of the screen in Windows 7, and I start a new instance of Calculator. I am trying to click and move the program window underneath the taskbar at the top. But as soon as I release the mouse button Windows pushes the program window out so that the titlebar is not obscured.
Clcik for a larger image.


Unexpected (unacceptable) behavior
I have now tested this in Windows 10 (1607). The problem arises when a child process is executed and places a new program window at Y coordinate 0, and the parent process is executed before the taskbar is placed at the top.
I used this bit of JS code to pop a new window from the web browser and place it at X=0 and Y=0 coordinates.
<!DOCTYPE html>
<html>
<head>
<script>
function myFunction()
{
var myWindow = window.open("", "Test Button", "left=0, top=0, width=200, height=200");
myWindow.document.write("<p>This is my test window at");
myWindow.document.write("<br>X coordinate: " + myWindow.screenX);
myWindow.document.write("<br>Y coordinate: " + myWindow.screenY + "</p>");
}
</script>
</head>
<body>
<style>
body {background-color: DarkOliveGreen;}
</style>
<button onclick="myFunction()">My Test Button</button>
</body>
</html>
Case 1:
- Set or leave the taskbar at the bottom.
- Open the HTML file.
- Click the button.
Windows should put your window at the very top of ths screen, in the upper left corner. For some reason my window was indented a few pixels to the right.

Case 2:
- Set the taskbar at the top.
- Open the HTML file.
- Click the button.
Windows should push your window down by 40 pixels, which is the height of the taskbar (when at the top or the bottom).

Case 3:
- Set or leave the taskbar at the bottom.
- Open the HTML file.
- Click the button.
- Set the taskbar at the top.
- Click the button again.
After the last step, you should find your window at the very top of the screen, underneath the taskbar with the window buttons inaccessible.

I still don't see this as a bug, but rather a design flaw. Regardless, it should have been corrected long since. If this has been around since Windows 95, then it means it has not been corrected for over 20 years. That's just unacceptable.
Solution
This is not exactly a solution but more of a workaround. One that the original poster has already mentioned.
- Press Alt + Space.
- Press M.
- Press Enter.

Note that you don't have to use the arrow keys to move the window.