If you can't even remember how you got the bitcoins, it's going to be hard. Can't you be sure you didn't just buy them on the platform with a bank transfer? Because you could know where to look at (your bank statements).
In 2013 there weren’t many platforms through which to buy Bitcoin using a bank transfer. I would say maybe not even one. it was a different time.
7 BTC is a huge amount of money, even in the current market crash.
At the moment (2013) when OP send 7BTC to Bitstamp, 1 Bitcoin was worth under $100. So at the time, the OP owned that Bitcoin, the value was not so big and certainly does not deserve special checks on how he bought them.
What they can ask them is only to confirm account verification, to make sure he was the original owner of that money.
OP, is there a possibility that you can access the address from which you sent that Bitcoin to Bitstamp? maybe that would help.