Theoretically possible in the sense that the lines exist and are connected? I don't know for sure, and while it may be a very convoluted route, I wouldn't be surprised.

EDIT: This map[1] suggests you could do Norwich -> Birmingham New Street -> Bristol Temple Meads. Without having to go through London, I suspect this is indeed possible without changing trains, even if no operator runs that route.

[1]: https://www.thetrainline.com/cmsmedia/cms/9384/national-rail...