Follow this procedure to create a private SSH key to be used for Github access from Cloud Build: https://cloud.google.com/build/docs/access-github-from-build
mkdir workingdir
cd workingdir
ssh-keygen -t rsa -b 4096 -N '' -f id_github -C <GITHUB_EMAIL>
This command creates a new SSH key id_github.
Add the public SSH key id_github.pub to your private repository's deploy keys.
Store the private SSH key in Secret Manager, in the github-key secret.
gcloud secrets versions add github-key --data-file=./id_github --project=$PROJECT_ID
After storing the secret, you can remove the local key file:
cd ..
rm -rf workingdir