Is your website live? If so, it could be showing up on Google already but lower on the list.
It's worth mentioning that one can't just "add" their website to Google searches. Google does it automatically based on a multitude of factors.
This is known as SEO.
Succinctly put, SEO is basically how easy it is to find your website on Google.
There are hundreds of strategies and techniques to boost your SEO, so it will require some researching and studying to learn how to improve your business' SEO.
The "Google Sale Channel" is something different, a priori it won't have a meaningful impact helping to show up your website on Google searches.
Kindly take a look into this link for further information regarding how to show up your website on Google searches.
Hi Steven (@Torpedofishing)
Welcome to the Shopify Community Forums! Thank you for sharing your question here with us to help with. I can definitely understand how important it is to make sure your site is discoverable on search engines like Google and there are a few steps you will need to take to make sure that happens.
The link that @diego_ezfy sent you is definitely a great place to start and I want to narrow it down to this article specifically: Help Center: Submitting Your Sitemap For Indexing. In order for your store to be searchable using a search engine you need to submit your store's sitemap (essentially a list of pages/content/URLs) for Google to index. Once indexed, Google will use a range of internal systems to show your website based on specific keywords used when customers are searching. If you have never done this before, don't worry. Our Help Center guide walks you through the process step by step and our support is here to help if you feel like you are stuck anywhere.
You also asked about the Google sales channel and if that was worth setting up. It 100% is! I would definitely encourage you to setup the Google sales channel to make use of our new partnership with Google and all the benefits the channel can unlock for your business.
The main benefits right now is that approved businesses receive free product listings across google, including google image search and maps! As we continue to grow this partnership, more and more benefits are going to be unlocked. This is also going to build your website trust with Google, which is really important.
I hope this information helps. Please let me know if you have any other questions about your website SEO I can assist with.