I'm Ava from Shopify Support.
I'm sorry to hear you're having some trouble here! I'm sure we can get to the bottom of this for you. Can you walk me through the steps you took to link your Google Merchant Centre account to your Shopify admin? Also, have you added the product's requirements that Google asks for in order to publish your products? There is a list of the requirements here! Products need to have information added to them so Google can classify them and approve them for sale. For example, if you sell products like apparel & accessories (clothing), Media, or Books, you will need to add product data on Age Groups, Sizing, Gender, & Colour before Google can approve the product. There is more information on that here. It is best to double-check that the product information you've added is correct.
Also, something to note, are you sure Google has finished reviewing your account? While Google reviews new Merchant Center accounts, they mark products as disapproved. Once the account review is complete, and if the account is in good standing, the products will automatically be resynced. Products that follow Google’s policies will change status to Approved shortly after. Any products that don’t follow Google’s policies will display reasons why they have been disapproved. It usually takes Google 3 - 5 business days to complete a review on an account. Can I ask when you synced your products?
Social Care | help.shopify.com