If your Omny Studio program and playlist are shared publicly, most likely your podcast is already indexed and active on Google Podcasts. You should not need to do anything.
You can verify your podcast is included in Google Podcasts by following this article.
Manual podcast submission
If your podcast is currently not included in Google Podcasts, you can submit your RSS feed to be manually crawled by Google using the "Submit to Google Podcasts" button.
Enhance your podcast on Google Search results
Google has an optional process to configure your podcast episodes to appear in the search results of your website on Google for Android devices.
Note: Even if you have correctly configured your website and feed, Google does not guarantee your podcast will appear in search results. The Google documentation writes "The Google algorithm tailors search results to create what it thinks is the best search experience for a user..."
To configure this, you must cross-reference your RSS's website link and your website's RSS metadata (you must have access to edit your website's HTML).
In Omny Studio, go to your playlist
In the "Details" tab, enter your website's URL in the "Website URL" field
3. On your website, include the a link reference to the Omny Studio playlist RSS feed. For example,
<link type="application/rss+xml" rel="alternate" title="Your Podcast's Name" href="https://omnystudio.com/d/playlist/XXX/podcast.rss"/>
Note: Google's requirements state you may only have one such link tag on your page. Many CMSs including Wordpress by default adds multiple links for your blog's RSS feeds.
You can read more about the requirements on the Google Podcasts documentation page.