How is it possible to see your car when you are in your car?
How is it possible to see your body when you are in your body?
How is it possible to see a crowd when you are part of a crowd?
You can’t, you can only see part of the Milky Way, the part you can see from the surface of the Earth, which is within the Milky Way, out on one of the arms.
When they show you “pictures” of the Milky Way, galaxy, though, that’s just a projection, they’ve taken what we know, and they’ve plotted it all so they can show what it might look like from “above” with a “you are here” arrow drawn on.
So when you look up at the night sky, if you can ever find a place that is low enough on light pollution that you can actually see it, what you see isn’t this big spiral… you’re right there in the midst of that, what you see is this:
A linear area with lots more light than the rest of the sky… looking a little like someone spilled some milk on your screen.