The Nintendo eShop is taking a hammering from Christmas crowds, resulting in the service going down. Nintendo actually issued a warning five days ago that this very thing might happen, but there is no doubt that plenty of gamers are feeling frustrated right now. This is pretty much guaranteed to happen at this time of year, unfortunately.
Nintendo consoles are commonly gifted as Christmas presents and with the competing Xbox and PlayStation consoles proving hard to get this year it is likely that Switch sales are higher than ever.
Nintendo is aware of the problem, as you would expect, but there isn’t much that they can do about it except wait for the crowds to all stop trying to squeeze through the door at the same time. They may have some emergency servers they can spin up to handle some additional load, but it is unlikely to be enough to allow everyone safe and seamless passage around the eShop right now.
You can keep up to date with how the eShop is doing by visiting the official Nintendo network information page that will be regularly updated with the network status. While it is certainly frustrating to not be able to set up your new Switch, you can always settle down with a nice Christmas movie and some chocolate while you wait.