How to get Google to know about my AWS Amplify Website

Ok, so I am a little confused on how to get Google (and other search engines) to know about and index my website. The website is a simple front-end React App.

According to my research, it seems like these are the steps I must take:

1. Create a sitemap.xml in the /public/index/ folder.
2. Submit the sitemap.xml to Google here: Google Search Console
3. And that is it?

So this is what I currently have:

I have my site hosted in AWS Amplify. If I navigate to my site's robots.txt file like this:

https://www.example.com/robots.txt

Then this is what the robots.txt file looks like:

# https://www.robotstxt.org/robotstxt.html
User-agent: *
Disallow:

So it's pretty empty. Is this OK? I have a feeling that file should have more info.

And this is my sitemap.xml file:

<?xml version="1.0" encoding="UTF-8"?>
<urlset xmlns="http://www.sitemaps.org/schemas/sitemap/0.9">
    <url>
        <loc>https://example.com/</loc>
    </url>
    <url>
        <loc>https://example.com.com/blog/</loc>
    </url>
</urlset>

What do I need to do to get my site noticed by Google and other search engines?