For example the bright royal blue color; R0 G10 B220, HEX: #000ae1. I know this color cannot be printed nor painted. But can this blue color exist in the real world other than on a digital screen? For example the aurora in the sky, or a rainbow in the sky?
You may wonder if there exists a material or non-electric light which looks the same as the said RGB screen blue. Of course that's perfectly possible.
In the beginning there's of course the blue cobalt glass. White seen through it is that quite high chromaticity blue. I guess you expected something less obvious than simple blue filtering. Here are some:
1: A natural crystal, water or diamond can act as prism which splits sunlight. With some lucky accident just the right wavelength could reach your eye and otherwise there is darkness due just as lucky screening obstacles. This way your eye can get the right excitation for the wanted sensation. You, the sun, a crystal and a hole in a wall just in right places.
2: There are self-illuminating materials. All of them actually are not self illuminating, they absorb other wavelengths which generate excited states into the electron structure of the material. As the time goes, the excited states collapse and radiation is transmitted. I can swear I have seen this color when I watched a black theatre show in Prague as a tourist. There strong ultraviolet lamps were used to create normally impossible light effects.
3: Strong radioactive radiation generates blue light in the water. Marie Curie noticed it 100 years ago in her Radium solutions. Pavel Cherenkov got his Nobel worthy ideas when watching the same phenomena.
4: Crime investigators in a tv-series seem to have some blood detecting spray which glows just that blue if there's blood. That's not imagination. The spray has chemical which is known as Luminol. It glows blue if there's present certain oxidization process starting materials. Blood is one of them. The chemical reaction makes the blue light.
5: In theory, hopefully not in practice we could see a cosmic item which reflects sunlight. This one approaches with velocity so high that the doppler shift makes it blue.
RGB is part of the light spectrum - it's essentially the visible portion of the spectrum. How light interacts with objects, how it is reflected, refracted, etc. and otherwise combined can easily create colors within the RGB spectrum for real-world situations. (In fact, one could argue that everything you see in the "real world" is an RGB color)
Realize that the entire light spectrum is vast - from Gamma Rays to AM - RGB is merely a small portion of the overall light spectrum.
I guess this is more a question on Physics and human perception.
"I know it can't be printed"
Well,... yes and no.
Physically, there is no reason why any RGB color could not be produced by paint or ink, provided good pigments and sufficient lighting on that paint/print.
Of course, not all pigments are easy to produce. Blue was historically the hardest. And still today, the dominant 4-pigment (CMYK) printing processes is weak in producing the saturated blues. But that doesn't mean that there aren't super blue pigments. Your LCD screen is using a phthalocyanine pigment to color its blue subpixels
Color by Structure
But even if pigments would fall short, then there's other options: Birds, butterflies and beetles can have a very bright blue thanks to diffraction on a microscopic scale structure (similar to the rainbow colors you see on a CD or DVD).
Emission vs. Absorption
A screen emits coloured light by itself, whereas the color of print or paint can only be observed if it is illuminated by an external light source. (In physical terms: The color on your screen is an emission spectrum. The color of paint or ink is an absorption spectrum). Even if you provide good lighting, then the human visual system will still perceive the colors differently (even if they measure the same). That's because the brain will take clues from the context to figure out that one is an emitted color and the other one is absorbed.