It is possible for Huawei, and Chinese companies in general, to build a successful alternative without using American technology (for the purposes of this post, I'm defining successful as equivalent to their American tech using competitors).
It's not possible.
What the actions on Huawei have done, however, is ensure that if that possibility exists, very significant chunks of Chinese resources will be devoted to finding it.
It appears China had decided this wasn't completely necessary, and were happy to rely on Americans for software, and core hardware. But that is obviously not true anymore, and the biggest long term effect of these actions are Chinese state resources being poured into directly combating and threatening American tech's competitive position.
And seeing that the tariffs and capricious action has not been limited to China, it won't even be surprising if some other nations join in to help, especially from the EU and/or India and Korea.