try cloud run

git init
npm init
npm i -S express

index.js

const express = require('express');
const app = express();

app.get('/', (req, res) => {
  console.log('Hello world received a request.');

  const target = process.env.TARGET || 'World';
  res.send(`Hello ${target}!`);
});

const port = process.env.PORT || 8080;
app.listen(port, () => {
  console.log('Hello world listening on port', port);
});

Dockerfile.

FROM node:10

WORKDIR /usr/src/app

COPY package.json package*.json ./

RUN npm install --only=production

COPY . .

CMD [ "node", "index.js" ]

gcloud config get-value project

gcloud builds submit --tag gcr.io/[PROJECT-ID]/helloworld
gcloud beta run deploy --image gcr.io/[PROJECT-ID]/helloworld