There are two things to check:
TPE 3D shows the Milky in two different ways depending on whether you're in Flying mode or Enhanced mode.
In Flying mode (default), the Milky Way is shown using a simplified representation that allows for quick navigation around the 3D scene:
The band of spheres you see heading upward to the left from the horizon represents the band of the Milky Way. The largest sphere is at the location of the Galactic Centre, which is where star density is at its highest (and there is usually the area that photographers prefer to capture in wide angle night photography).
To see the full star map, press the 'Enhance' button on the right of the screen:
In Enhanced mode, the simplified representation is replaced with a detail view of the night sky. As you can see the band of the Milky Way aligns with the simplified representation shown above, but now you can see the Milky Way as it actually appears in a clear, dark sky.
Location and Direction of view
The second thing to check, if you're not seeing the Milky Way when you expect to, is your location and direction of view.
The centre of the Milky Way is never visible beyond around 60 degrees north due to the orientation of the earth. That's why you see few Milky Way shots from Iceland (only the less dense parts of the Milky Way band are ever visible that far north). Even at the summer solstice, when the tilt of the earth is most inclined towards the Galactic Centre (centre of the Milky Way), the core lies below the horizon at transit (the time when it is highest in the sky each day, more or less). Additionally, the sky is not even close to being dark. Here we are looking at the Galactic Centre from Vik, south Iceland, on June 21 - not much to see!
Later in the year, the skies darken, but transit occurs earlier in the evening before the sun has set. We can see a glimpse of the Milky Way later in the evening, but it dives out of sight quite quickly:
Even if you're in classic dark sky locations such as Muley Point, Utah or Uluru, Australia, the direction you need to look for the Galactic Centre varies. In general, in the Northern Hemisphere, you should look south, and vice versa in the Southern Hemisphere.
Compare these two views:
The first is looking south from Muley Point, Utah. The Galactic Centre lies only a few degrees above the horizon:
On the same date at Uluru in Australia's Northern Territory, the Galactic Centre lies to the north and very high in the sky:
If you need a pointer to where the Galactic Centre is at any time, then in Flying mode, you can literally tap the pointer!
After tapping it, the camera will be tracking the Galactic Centre as you adjust time or date (or even camera location and zoom):