The clock starts ticking after you sign up for Google's cloud platform, not when you create an API key. This being said, try the following:
1. Try to access the API via your web browser: https://translation.googleapis.com/language/translate/v2?key=YOUR_API_KEY_HERE&source=en&target=es&q=cow
If you still get a 403 error, it's def. a problem with your key.
2. Make sure you've the translation API enabled https://support.google.com/cloud/answer/6158841?hl=en