Expose Both Ports 8080 and 3000 For Cloud Run Deployment

TL:DR - I am trying to deploy my MERN stack application to GCP's Cloud Run. Struggling with what I believe is a port issue.

My React application is in a client folder inside of my Node.js application.

Here is my one Dockerfile to run both the front-end and back-end:

FROM node:13.12.0-alpine
WORKDIR /app
COPY . ./

# Installing components for be connector
RUN npm install --silent  
WORKDIR /app/client
RUN npm install --silent

WORKDIR /app
RUN chmod +x /app/entrypoint.sh
ENTRYPOINT [ "/app/entrypoint.sh" ]

... and here is my entrypoint.sh file:

#!/bin/sh
node /app/index.js &
cd /app/client
npm start

docker-compose up works locally, and docker run -p 8080:8080 -p 3000:3000 <image_id> runs the image I built. Port 8080 is for Node and port 3000 for the React app. However, on Cloud Run, the app does not work. When I visit the app deployed to Cloud Run, the frontend initially loads for a split second, but then the app crashes as it attempts to make requests to the API.

In the Advanced Settings, there is a container port which defaults to 8080. I've tried changing this to 3000, but neither works. I cannot enter 8080,3000, as the field takes valid integers only for the port. Is it possible to deploy React + Node at the same time to Cloud Run like this? How can I have Cloud Run listen on both 8080 and 3000, as opposed to just 1 of the 2?

Thanks!