The costs you are talking about is also known as CAC - customer acquisition costs. There is literally *no* business where CAC is zero. You spend salespeople's time, marketing $s, advertising, or other $s to acquire this customer.
CAC is therefore always an operating cost and below the line (underneath COGS).
Fixed and Variable costs are about producing the product OR service - i.e., how much does the company spend to create what someone will buy. It is purely a part of COGS.
CAC is about getting that product/service into a customer's hands.
As companies grow, CAC usually goes DOWN even if their company size grows, but it varies if you are an enterprise or a consumer company. SNAPCHAT spends lot less to get a new user now because there is so much more word of mouth. On the other hand, Salesforce is now going after bigger and bigger companies to sell to, so their avg CAC may be going UP.