Is there a way to manage stock levels?
Yes, you are correct: The quantity available for a product is not considered a product attribute. A product attribute is, for example, color, size, weight. The quantity available in store is a value associated with the store, not an intrinsic property of the product.  

Using only Drupal Commerce, you cannot manage stocks. There is a Commerce Stock module, but it just has only a development snapshot, for Drupal 8, which has been updated on November, 2017.


  The stock module does two main things
  
  
  Maintain stock levels
  Implement validation of stock to prevent users from ordering out of stock items
  
  
  The module does the following stock validation checks
  
  
  Disable the add to cart button for out of stock products
  Validates the add to cart quantity widget
  Checks current Cart quantity when adding to your cart (so if stock is 10 and you got 6 in your cart you can only add 4)
  Checks that all products and quantities in the shopping cart (/cart) are in stock
  On Checkout if you attempt to enter, continue or complete with out of stock items you get redirected to the shopping cart