Two that come to mind are Coinbase & Circle. I did a quick google search, possibly wrong terms. The information I got was useless. I am sure this has been discussed. If there is a good article/link on this it would be appreciated.
I think that they have earned those bitcoin from users but also I believe that someone on their team is one of the early adopters.
They probably have invested a lot in the early stages of bitcoin or and are big investors and have bought bitcoin when the price was cheaper.
Because they are an exchange they get profit from exchanges that make users and they usually take fees from 0.2% up to 1%.
Obviously they start with a few bitcons and in time earn more by charging their traders fees on trade they made. From there that stack of bitcoin keeps growing and most of th eexchagnes invest in better security, more usability and even hire more developer to add more coins and/or support employee to improve their support.