I recorded a video with the webcam.
I did this with LogiCapture. The sound already comes within LogiCapture via my sound interface.
Just dragged this video onto a track in ShotCut.
The first 2 seconds are totally krankt, then the sound absolut is ok.
Check if the video of your recording is really ok. You can do that with Audacity or with VLC-Player. With a high-quality Panasonic G9, the beginning (1 sec.) is always somewhat disturbed. It could be that your problems are not caused by Shotcut, but by your camera.