The recommended solution is to go with WP Pusher. It is easy and quick to deploy automatically from GitHub or other services. The first step is to download the WordPress plugin from: https://wppusher.com/
Then navigate to your WordPress administration on your live site and install the downloaded plugin: Plugins -> Add New -> Upload Plugin -> Install Now.
Activate the plugin and navigate to the plugin page WP Pusher . Click on the GitHub or any other tab and obtain a token by pressing the button on the page, then copy and save the token.
At this point go to your terminal, navigate to your WordPressify project and generate your distribution files with the command:
npm run prod
Navigate to your theme distribution files on:
Create a git repository and push all the files on GitHub. This repository will have only the theme distribution files.
Once the files are on GitHub you can get back to the WordPress administration on the WP Pusher plugin page and follow the Next Steps, click on Install a theme.
On Repository host we choose GitHub, then click on Pick from GitHub and choose the newly created repository with the distribution files. Then install & activate the theme.
Push-to-Deploy if you want automatic deployments to happen when you do a push to the distribution repository. In this case you have to create a Webhook from your GitHub’s repository page.
First navigate to the WP Pusher plugin page and click on Themes, it will show you the list of the templates you have installed through the plugin itself. Click on Show Push-to-Deploy URL to get the Payload URL.
Now get back to GitHub and navigate to your distribution repository and click on: Settings -> Webhooks -> Add webhook. Now past the URL and click Add webhook.
This should enable automatic deployment on any push to the chosen GitHub repository.
Note: WP Pusher if free only with public repositories.