I had to look it up, there is no external wired remote port for a D3400. The hot-shoe does not control shutter release.
So you either find a wireless infrared shutter release remote with an intervalometer and live with a max 30 second exposure time per frame, or use a laptop pc by USB cable and control with DigiCam Control. I don't think there is a product to do the wireless option.
Edit: Just checked digicamcontrol camera chart. D3400 cannot use Bulb mode from software, so we get the 30 second max exposure time that way also. Looks like Nikon does not want that camera used for advanced astrophotography.
I will add that I have not used a tracker for a Milky Way landscape shot. I shoot those with an ultra wide lens on tripod, and set exposure time at 10 to 15 seconds. But the upgraded Nikons also have an intervalometer feature built-in to do that. And a port to plug in a remote shutter release for Bulb mode.