Well first you wanna make sure you have at least a nat b type, (In my opinion, A is rare and I never had it but not required) Anything lower than C is probably bad. Second, make sure you have least 10 MBPS upload and download. Third, maybe is just your hot spot, not sure if it is dual band or not, try both, who knows. Having a router allows to setup stuff to the user need, such as ports which is important. If you need more help, go to the nintendo support website for info.
First make sure you can even connect to the internet, go to settings and do a test, then connect to e-shop, next download any game updates that may be required. (Press start or "+" on any game in the home menu and press software update) If all else fails, check to see if the service is not offline or maintenance or something and restart the switch.
In the end it could be defective and just need to be serviced by nintendo, take it back to the store and exchange it maybe.