Can secondary colors be created without using any primary colors?

yes they can

Explanation:

The secondaries of a given primary set cannot be mixed to create the primaries of that set; they can mix to create a color of the same hue, but at a lower saturation (saturation is the parameter which corresponds to the “purity” of the color, how well it approximates a single wavelength of light).

Explanation:

This is because the color gamut enclosed by the secondaries must lie within the gamut of the primaries, and the primaries themselves will lie outside that “secondary gamut.”

Another way to look at this: consider a typical RGB set of primaries. We can obtain yellow by mixing red and green, and magenta by mixing red and blue. But in mixing the yellow and magenta to try to get back to red, you wind up with a combination that is mostly the original red but still with some green and blue content. Hence you would have a color which is the same hue (dominant wavelength) as the red, but moved toward white (a more “pinkish” shade).