Steam now lets you easily see when you bought a game. Just visit this link and then login with your Steam credentials. You will be presented with your purchase history along with the date of when you bought that game.
Or if that’s not possible then follow these below steps.
Steam How to find out when you bought a game
- Open the Steam client or visit the website
- Click on your account name
- Click on ‘Account Details’
- Select ‘View purchase history’