Is it possible to embed the store into my google sites web page, I would like the user experience to be in one place not push them to store.link site then have to create a link to push back to my google sites page.
Yes you can embed the Store by URL or using Iframe in Google Sites.
You can create a new Page or on your existing Home Page, you can click on Embed and then it will show two options.
Choose By URL, then paste your URL and click on Whole Page and Insert.
That will add the store. You can change the height as required.
Hope this helps.
Aslam