First, the NWU info on Nikon USA doesn't say it is compatible with the D3300 camera, but we can try. Which version of Windows do you use? It may need to be 10. Are you using the latest firmware for the camera? Make sure it is. If you just downloaded the Nikon Webcam Utility (NWU) then that should be okay. With the camera off, put in a working memory card, it may be necessary even if you are not using it. If you can take a pic on AUTO mode, it should be fine with the card and lens (< 50mm) that you are using. Take a pic and see. Connect the cable and turn the camera on, with NWU installed. What options pop up in Windows, and which do you select? Try to use Zoom, Skype, or facebook video and see if you can talk with someone. OBS may not be a compatible program with your camera, so for now, don't use it. With Nikon, sometimes you have to use specific programs, and do things in a specific order in order for them to work. For example, having the camera on and plugging it in may not work. The battery also has to at least be close to fully charged to be sure it will work. Auto focus may need to be S, not continuous. There may be other solutions that members here know, give them a few days as not everyone comes here every day. I hope this helps!
Rob