It is more complicated than this as the atmosphere of the earth also creates its own light (since it has a temperature it emits radiation like a blackbody, and there are many processes known as airflow that emit light too, it's just very faint).

But to keep it simple:

What colour is the sky at night? Black, which is the absence of light (you're basically looking at space).

When light from the sun (which is composed of all wavelengths of light, emitted roughly like a blackbody) reaches the atmosphere a few things can happen to it based on the wavelength of light, and because of the atoms and molecules present in the atmosphere.

It can scatter (think of a small ball bouncing off a bunch of bigger balls in all directions)

It can be absorbed (the energy from the light is absorbed by an atom/molecule increasing its temperature/kinetic energy, or exciting the atom/molecule into a higher energy state, potentially being released as a different wavelength of light.

It can be deflected/refracted, thereby changing the direction of the light

Or it can pass through.

It's more complicated than this but we will go with it for now.

Because all of these are dependent on the wavelength of light, different colours will behave differently. At noon, the amount of atmosphere the sunlight passes through is at a minimum, and due to the chemical composition of our atmosphere, the only wavelengths (in the visible wavelengths) that pass through almost freely are the ones on the red side. So, the blue is scattered, and inevitably some is scattered into our eyes.

During sunset, there is so much atmosphere between you and the sun, even the red wavelengths are scattered.

What determines which is scattered? Different atoms/molecules have different physical sizes, So a big molecule will scatter wavelengths smaller than it.

And, blue is smaller than red (400nm vs 650nn).

I hope that helps and isn't too much.

Tldr;

No

This may be slightly simplistic

Sky is made of air. Air is colourless, and space is black. So it has to be the sunlight hitting the air to cause the colour. During most of the day, the sun hitting the air makes it look blue. When the sun is at a different angle, such as dawn and dusk, it looks red/orange. The chemical composition of the air doesn't change, nor does the colour of space. The only thing that's changed is the angle/amount of sunlight. Thus, we can infer that while the sky appears blue, it's not due to it being inherently blue, but rather it's blue due to sunlight hitting it at specific angles.

If you were observing the same orange sunset a couple time zones away, under the same sky, made of the same oxygen, nitrogen and carbon dioxide, at the same moment in time, it could be mid afternoon and the sky is perfectly blue.