Dallas here from Shopify Social Care.
Are you referring to Adsense or Google Ads?
If you are referring to Google Ads you can actually set that up in your Shopify Admin. All your Google Ads can be created under Marketing in your Store Admin. The marketing tool was set up recently so you don't have to worry about dealing with a third party website. This link here will go into a bit more detail about creating a Marketing Campaign with Shopify.
This link here will go into more detail about how to make Google Ads specifically and how to set them up. It even has a video (only 57 seconds) that I definitely recommend.
If you would like I can try and help you figure out some good options for marketing your store. Are you able to tell me what steps you have taken so far?
I look forward to hearing back from you,