...Really, the shape of the forward viewing thing might even suggest that there are no portholes of any sort on the shuttle - just fancy black paint on a solid hull. After all, the viewer appears to be nearly vertical, rather tall, and fails to reveal any of the long and pointed nose even when the "camera" is set relatively high. So, a viewscreen rather than a windshield?
(That would go nicely with your idea that the craft is of Vulcan descent, considering the number of Vulcan shuttles that lack windshields.)
The alternative interpretation is that we see a wraparound windshield corresponding to the external shape - but it is well separated from Sulu's console, perhaps more than a meter ahead of it, and the perspective of the animation isn't picture-perfect... That is, there are side sections to the windshield, but even those are far ahead of Sulu's position and merely allow him a view to lower forward quarters.