There isn’t a practical interchangeable lens for your D3400 that truly matches the Nikon P1000 at its longest setting.

The P1000’s headline reach comes from combining a relatively small actual lens with a very small sensor, giving a very narrow field of view equivalent to about 3000mm on full frame. On a D3400, the longest realistic DSLR option is more like a Nikon 200-500mm f/5.6, which gives roughly an 800mm full-frame equivalent field of view on APS-C.

You can go longer with exotic super-telephoto lenses, telescopes, or by stacking teleconverters, but those setups are typically very large, expensive, slow, hard to handhold, often manual focus, and can be mechanically awkward.

So the closest practical answer is: use a long telephoto such as a 200-500mm lens and crop when needed. You won’t equal the P1000’s maximum reach, but you may get better image quality, less noise, and a sharper result at more moderate focal lengths. The P1000’s real advantage is that its lens, stabilization, and camera are all designed together specifically for extreme zoom.