Important Note: Orders captured through Buy on Google and within your Google Merchant Center account are imported every 10 minutes automatically by Sales & Orders. Please allow for at minimum 15 minutes and at maximum 30 minutes for the order to be built in your store control panel.
In Google Merchant Center you can view orders from Buy on Google - this information is also stored in your S&O account as well.
Log into Merchant Center
Under Orders click All Orders
You can toggle between orders "PENDING SHIPMENT", "PENDING DELIVERY", or "ALL ORDERS":
Click on the Google order ID to access the order's details. Again, all this information is imported directly into your Sales & Orders account.
As order statuses change inside your store, S&O will export and update order details within Merchant Center.