We don't for sure as our vantage point does not allow us to determine that. However, by viewing other spiral galaxies (Andromeda, Sombrero galaxies) we can make a calculated guess that our galaxy is shaped in the same way.
Also, while we can't see the galaxy as a whole, what we can see is consistent with it being a flat disk... specifically, we can even tell that it appears to be a barred spiral galaxy.
spiral arm
When seen edge-on, a spiral galaxy appears as a thin, flat disk with a bulging central region. The disk is often darkened by dust lanes along its plane, giving it a more defined edge. The spiral arms are not visible from this perspective.
Galaxies are flat because of the way gravity and angular momentum interact during their formation. As gas and dust collapse to form a galaxy, the rotation causes it to flatten out into a disk shape. This rotation helps balance the inward pull of gravity, resulting in a flat, disk-like structure.
The Milky Way is both disk-like and spiral in shape. It is a barred spiral galaxy, meaning it has a flat, rotating disk with spiral arms emanating from a central bar. This shape is common among spiral galaxies due to the rotation of stars and gas in the galaxy.
A huge spiraling disk of stars, dust, and gas is called a galaxy. The Milky Way is an example of a galaxy that contains our solar system.
The axis plane of the solar system is tilted by about 60 degrees relative to the average plane of the Milky Way galaxy. This means that the solar system is not perfectly aligned with the flat disk of the galaxy but is slightly inclined.
A "spiral" galaxy.
A disk
what is the thin gas and clusters of stars surrounds the disk of the Milky Way Galaxy.
The galaxy is flat because of the way it formed and rotates. As the galaxy spins, gravity pulls the stars and gas towards the center, creating a flat, disk-like shape. This rotation helps maintain the flatness of the galaxy over time.
Most galaxies are shaped like a disk. It's the way they are formed. One of the most beautiful is the Sombrero Galaxy. [See related link for a picture]
They are shaped like a round galaxy and they are flat