Is it possible to build SharePoint Framework Web Parts without using NodeJS, Yeoman, gulp?
The three components included in the Microsoft SPFx framework are npm (the package manager), Yeoman (the scaffolding tool), and Gulp (the build system). You could ostensibly do manually what each of these tools automates for you, but it would be quite difficult. I understand there is some support for alternatives coming (e.g. Yarn instead of Gulp).