Alpine linux in Docker container => `env: can't execute 'node': No such file or directory`

The Alpine distro is based on a libc variant called musl-libc. The node binary you are installing is compiled against glibc, as most (all?) other standard distros use the more commonly used glibc standard library.

One option is to add glibc to your alpine distro base, and then if you were truly unable to compile node against musl-libc you could allow the glibc support you added handle the mismatch. There are other stackoverflow answers which provide details on how to do this.

However, I think the best case scenario is for you to use a node binary built against Alpine's musl-libc. This is the way the official node images handle the alpine tag variant. You can see how they do that here in the official Node 12.4.0 release Dockerfile for node's alpine variant. Of course your build will be longer to build node versus download a pre-built binary, but it will simplify any complications around trying to shoehorn glibc support into Alpine.