Mentioning the sum of $1K to buy Bitcoin is a bit complicating because from an onset up to date Bitcoin has always been possible to buy in any amount. Perhaps... If you are unable to buy a whole 1 Bitcoin you can as well buy some fractions of it Satoshi.

But if I get to be dynamic in thought, yes of course you can and at then trading as buying and selling of Bitcoins was not of todays technologies where exchange and platforms has been made possible and accessible for everyone.

Around 2010 based on my research to how to acquire and buy Bitcoin was through online negotiations as P2P in reputable platforms like here the bitcointalk platform and some other Internet related contacts such as one-on-one negotiate which payments has formally been without escrows which role the exchanges has come to play to grant fair transaction deals in the P2P.