How to install node 16 inside of a buildspec yaml's install step within an Alpine Linux container?

Question

I have a buildspec (v 0.2) file that will be deployed and built using CodeBuild. Inside of my deploy file I am using a very specific image (cant be changed) and it is an alpine linux container. In there, I need to run some npm commands in the build step within the deploy.yml file. The image I am using does not support the runtime_version option so I am trying to install node 16 directly in the phases -> install -> commands: section of the file. But when I run my deploy step, it is failing to properly link nodejs because when I run node -v the CodeBuild logs indicate that node is not found. What do I need to tweak here to make the deploy find node and npm? Thanks.

Error output from logs:

[Container] 2023/06/22 17:25:22 Running command apk update
fetch https://dl-cdn.alpinelinux.org/alpine/v3.17/main/x86_64/APKINDEX.tar.gz
fetch https://dl-cdn.alpinelinux.org/alpine/v3.17/community/x86_64/APKINDEX.tar.gz
v3.17.4-19-g2ae254083c3 [https://dl-cdn.alpinelinux.org/alpine/v3.17/main]
v3.17.4-16-gf6cb711c1a3 [https://dl-cdn.alpinelinux.org/alpine/v3.17/community]
OK: 17840 distinct packages available

[Container] 2023/06/22 17:25:23 Running command apk add --no-cache curl python3 make g++
fetch https://dl-cdn.alpinelinux.org/alpine/v3.17/main/x86_64/APKINDEX.tar.gz
fetch https://dl-cdn.alpinelinux.org/alpine/v3.17/community/x86_64/APKINDEX.tar.gz
(1/4) Installing libstdc++-dev (12.2.1_git20220924-r4)
(2/4) Installing libc-dev (0.7.2-r3)
(3/4) Installing g++ (12.2.1_git20220924-r4)
(4/4) Installing make (4.3-r1)
Executing busybox-1.35.0-r29.trigger
OK: 1213 MiB in 82 packages

[Container] 2023/06/22 17:25:24 Running command curl -o node.tar.xz https://nodejs.org/dist/v16.19.0/node-v16.19.0-linux-x64.tar.xz
  % Total    % Received % Xferd  Average Speed   Time    Time     Time  Current
                                 Dload  Upload   Total   Spent    Left  Speed

  0     0    0     0    0     0      0      0 --:--:-- --:--:-- --:--:--     0
100 21.4M  100 21.4M    0     0  92.2M      0 --:--:-- --:--:-- --:--:-- 92.4M

[Container] 2023/06/22 17:25:24 Running command tar -xf node.tar.xz

[Container] 2023/06/22 17:25:26 Running command mv node-* /usr/local/node

[Container] 2023/06/22 17:25:27 Running command ln -s /usr/local/node/bin/node /usr/bin/node

[Container] 2023/06/22 17:25:27 Running command ln -s /usr/local/node/bin/npm /usr/bin/npm

[Container] 2023/06/22 17:25:27 Running command export PATH="/usr/local/node/bin:$PATH"

[Container] 2023/06/22 17:25:27 Running command node -v
/codebuild/output/tmp/script.sh: line 4: node: not found

[Container] 2023/06/22 17:25:27 Command did not exit successfully node -v exit status 127

Relevant buildspec deploy.yml

version: 0.2

phases:
  install:
    commands:
      - apk update
      - apk add --no-cache curl python3 make g++
      - curl -o node.tar.xz https://nodejs.org/dist/v16.19.0/node-v16.19.0-linux-x64.tar.xz
      - tar -xf node.tar.xz
      - mv node-* /usr/local/node
      - ln -s /usr/local/node/bin/node /usr/bin/node
      - ln -s /usr/local/node/bin/npm /usr/bin/npm
      # This line was added to set the PATH variable
      - export PATH="/usr/local/node/bin:$PATH"
      - node -v
      - npm -v

UPDATE ATTEMPT #2:

From my build.yml file I try calling a bash script from the phases/install/commands section. It get's into the bash script and runs it (purpose is to install node using nvm) and it installs but when node --version is ran it still errors out.

install_node.sh

#!/bin/bash

# Install required packages
apk update
apk add --no-cache curl bash

# Install NVM
curl -o- https://raw.githubusercontent.com/nvm-sh/nvm/v0.39.0/install.sh | bash

# Check if a profile file exists
if [ -f ~/.bashrc ]; then
  echo "Profile file ~/.bashrc already exists."
else
  echo "Creating profile file ~/.bashrc."
  echo "export NVM_DIR=\"$HOME/.nvm\"" >> ~/.bashrc
  echo "[ -s \"$NVM_DIR/nvm.sh\" ] && \. \"$NVM_DIR/nvm.sh\"" >> ~/.bashrc
fi

# Activate NVM
export NVM_DIR="$HOME/.nvm"
[ -s "$NVM_DIR/nvm.sh" ] && \. "$NVM_DIR/nvm.sh"

# Install Node.js
nvm install 16.19.0

# Set the installed version as the default
nvm alias default 16.19.0

# Set the PATH environment variable
export PATH="/root/.nvm/versions/node/v16.19.0/bin:$PATH"

# Install Sudo
apk add sudo

echo "CHANGING PERMISSIONS TO EXECUTE NODE BINARY"
# Make the node binary executable
sudo chmod +x /root/.nvm/versions/node/v16.19.0/bin/node

# Check the permissions of the node binary
echo "CHECKING TO SEE IF THIS HAS PERMISSIONS TO EXECUTE NODE BINARY"
ls -l /root/.nvm/versions/node/v16.19.0/bin/node

node --version

Thanks!