No chance of damage (the giantness of the telescope makes little difference!), but these cameras can not shoot at a shutter speed of 1/1000 second, so the lit part of the Moon is out of reach due to overexposure.
Can large scientific telescopes observe the moon...
The bright part will probably be too bright to easily image with a deep field camera because it's designed for integration times of seconds to minutes.
The hardware won't be able to provide a 1/1000 second exposure, so only objects in shadows (or the unlit side of the Moon) have a chance of being exposed.
When I look at the full moon through my 10cm telescope, it is so bright that it hurts
Because of conservation of etendue (see below) the Moon has the same surface brightness when seen through any telescope or binocular. It's just that it's bigger and so is spread over a larger area of your retina.
It's just like looking at 100 full Moons in the sky, but each Moon is no brighter than the one we see now.
Put in less than precise but simple wording, magnification increases the size, but not the apparent brightness per unit area of extended objects.
...without being damaged?
There's no chance of damage.
This answer to Can a telescope ever increase the apparent luminance of an extended object? says No and explains that this is the result of conservation of etendue
In big telescopes, the focal planes are also pretty huge.
(units: mm) aperture focal length f/no.
Human eye 6 17 2.8
Vera C. Reuben telescope 8,360 10,310 1.23
So per square micron, the image of the moon will be $(2.8/1.23)^2 \approx 5$ times brighter on the worst case1 telescope's focal plane than on our retina (seen through a telescope or by eye), that's not going to hurt the silicon.
After all we often take outdoor photos with the Sun in the field of view and that doesn't even melt the polymer coatings and color filters on top of the CCD!
1lowest f/no. big telescope so brightest per unit area on the sensor.
Suzanne Jacoby with the LSST focal plane array scale model. The array's diameter is 64 cm. This mosaic will provide over 3 gigapixels per image. The image of the moon (30 arcminutes) is present to show the scale of the field of view.