Alright, let's kick things off by creating a new Vue.js project using Vue CLI. If you don't have a project yet, no worries, we'll get you set up.

npm install -g @vue/cli
vue create my-ssr-vue-app
cd my-ssr-vue-app

Next up, we need Nuxt.js. It's a fantastic framework built on top of Vue.js that helps with server-side rendering (SSR). Let's add it to our project.

npm install nuxt

Now, we need to tweak the package.json file a bit to include scripts for starting Nuxt:

"scripts": {
  "dev": "nuxt",
  "build": "nuxt build",
  "start": "nuxt start"
}

And don't forget to create a nuxt.config.js file for your Nuxt.js configurations:

export default {
  target: 'server',
}

Time to build your Vue.js app! Follow Nuxt.js conventions and create your app within the pages directory. For instance, let's create pages/index.vue:

<template>
  <div>
    <h1>Welcome to Nuxt SSR with Firebase Hosting</h1>
  </div>
</template>

<script>
export default {
  name: 'IndexPage',
}
</script>

Make sure you have the Firebase CLI installed. If not, let's get that sorted out:

npm install -g firebase-tools

Log in to Firebase and initialize a new Firebase project within your my-ssr-vue-app directory:

firebase login
firebase init

During the setup, choose options for Firebase Hosting and Functions. When asked for the public directory, set it to dist.

Head over to the functions directory created by Firebase, and install the necessary dependencies:

cd functions
npm install express nuxt

Now, let's modify functions/index.js to set up the Nuxt.js app with Express:

const functions = require('firebase-functions');
const express = require('express');
const { Nuxt } = require('nuxt');
const nuxtConfig = require('../nuxt.config.js');

nuxtConfig.dev = false;
const nuxt = new Nuxt(nuxtConfig);

const app = express();

app.use(nuxt.render);

exports.nuxtApp = functions.https.onRequest(app);

Let's tweak the firebase.json file at the root of your project to route Firebase Hosting to Firebase Functions. Remove any unnecessary settings like the public directory configuration:

{
  "hosting": {
    "rewrites": [
      {
        "source": "**",
        "function": "nuxtApp"
      }
    ]
  },
  "functions": {
    "source": "functions"
  }
}

Finally, build your Nuxt.js application and deploy it to Firebase Hosting:

npm run build
firebase deploy

And there you have it! Your Vue.js application with server-side rendering should now be up and running on Firebase. Enjoy!