So far, regular keys can only be bought with money or traded for. Psyonix did recently add limited items called Decryptors that can open crates and be earned through normal play.
The way it works is there is an established event period, during which playing games earns you a limited in-game currency (e.g., they had a Halloween event where you earned candy corn). Once you amass enough of that currency, you can use it to purchase Decryptors and some other limited items (e.g., toppers, decals, etc.). Decryptors can open any crate, but the catch is that any item you receive is locked to your account, so it can't be traded.
There is no event happening at this time, but there will likely be one sometime in the spring. Hope that helps.