Google Cloud Build - firebase deployment error: "public directory 'dist/browser' does not exist, can't deploy hosting to site PROJECT-ID"

I´m trying to simultaneously deploy my Angular Universal web-app to Cloud Run (for SSR) and Firebase Hosting (for caching). The deployment to Cloud Run works fine and I followed this guide (https://cloud.google.com/build/docs/deploying-builds/deploy-firebase#using_the_firebase_community_builder) to enable Firebase deployment with Google Cloud Build.

However, whenever I run gcloud builds submit --config=cloudbuild.yaml the error: public directory 'dist/browser' does not exist, can't deploy hosting to site PROJECT-ID is thrown during the Firebase deployment step in the cloudbuild.yaml.

cloudbuild.yaml:

steps:
  # build image
  - name: 'gcr.io/cloud-builders/docker'
    args: [ 'build', '-t', 'gcr.io/PROJECT-ID/SERVICE-ID', '.' ]
  # push image
  - name: 'gcr.io/cloud-builders/docker'
    args: ['push', 'gcr.io/PROJECT-ID/SERVICE-ID']
  # deploy to Cloud Run
  - name: "gcr.io/cloud-builders/gcloud"
    args: [ "run", "deploy", "SERVICE-ID", "--image", "gcr.io/PROJECT-ID/SERVICE-ID", "--region", "us-central1", "--platform", "managed", "--allow-unauthenticated" ]
  # deploy to Firebase (ERROR HAPPENS HERE Specified public directory 'xx' does not exist, can't deploy hosting to site PROJECT-ID)
  - name: gcr.io/PROJECT-ID/firebase
    args: ['deploy', '--project=PROJECT-ID', '--only=hosting']
images:
  - 'gcr.io/PROJECT-ID/SERVICE-ID'
timeout: 1800s
substitutions:
  _ENV_VARIABLE: development

Dockerfile

FROM node:14

# set work directory
WORKDIR usr/src/app

# copy package.json and package-lock
COPY package*.json ./

# install dependencies
RUN npm install

# copy local code to container
COPY . .

# build app
RUN npm run build:ssr

# serve app
CMD ["npm", "run", "serve:ssr"]

firebase.json

{
...
  "hosting": [
    {
      "public": "dist/browser",
      "ignore": [
        "**/.*"
      ],
      ...
    }
  ]
...
}

error-log

DEBUG: https://storage.googleapis.com:443 "GET /987290120943.cloudbuild-logs.googleusercontent.com/log-93082fbf-1b87-499a-9132-fed5f1c06aad.txt HTTP/1.1" 206 290
DEBUG: Reading GCS logfile: 206 (read 290 bytes)
Step #3:
Step #3: ←[1m←[37m===←[39m Deploying to 'PROJECT-ID'...←[22m
Step #3:
Step #3: ←[1m←[36mi ←[39m←[22m deploying ←[1mhosting←[22m
Step #3:
Step #3: ←[1m←[31mError:←[39m←[22m Specified public directory 'dist/browser' does not exist, can't deploy hosting to site PROJECT-ID
DEBUG: https://cloudbuild.googleapis.com:443 "GET /v1/projects/PROJECT-ID/locations/global/builds/93082fbf-1b87-499a-9132-fed5f1c06aad?alt=json HTTP/1.1" 200 None
DEBUG: https://storage.googleapis.com:443 "GET /987290120943.cloudbuild-logs.googleusercontent.com/log-93082fbf-1b87-499a-9132-fed5f1c06aad.txt HTTP/1.1" 206 120
DEBUG: Reading GCS logfile: 206 (read 120 bytes)
Finished Step #3
ERROR
ERROR: build step 3 "gcr.io/PROJECT-ID/firebase" failed: step exited with non-zero status: 1
DEBUG: https://storage.googleapis.com:443 "GET /987290120943.cloudbuild-logs.googleusercontent.com/log-93082fbf-1b87-499a-9132-fed5f1c06aad.txt HTTP/1.1" 416 168
DEBUG: Reading GCS logfile: 416 (no new content; keep polling)

Since everything works fine locally, I assume that it may have to do something with gcr.io/PROJECT-ID/firebase being in a different container than the service gcr.io/PROJECT-ID/SERVICE-ID where perhaps the dist folder is created.

Edit #1:

I tested creating a folder called "static" in the root of the project and changed the public property in firebase.json to 'static'. It worked which makes me believe that for some reason the dist/browser directory does not exist during the "deploy to Firebase" step in the cloudbuild.yaml even though it is created during RUN npm run build:ssr of the Dockerfile.

Edit #2:

I found something not quite adequate (https://stackoverflow.com/a/64215324/8581106) on a similar problem. However, the suggestion seems to be to also run the build command npm run build:ssr before the Firebase deployment in the cloudbuild.yaml to make sure the dist/browser directory exists. But I´d really like to avoid serving one build on Cloud Run and deploy a new build to Firebase, because Angular uses unique hashes for .js and .css files everytime and I feel like this could lead to caching problems.

Edit #3:

I created an image to visualize my problem better (see image below). I´m new to docker and Cloud Build, but I feel like this is the procedure when I run gcloud builds submit --config=cloudbuild.yaml. I don´t understand why the dist/browser exists in the Dockerfile scope but not in the cloudbuild.yaml scope.