Ensure your game is patched to v1.4 . You can find the Rest of Europe (ROE) patch and North American patches on sites like Archive.org or EA Forums .
If you are using a standard Cheat Engine trainer (like the one by rcgldr), the process is straightforward: Need For Speed Carbon Trainer 1.4 Unlock All Cars
A dedicated trainer platform that provides a verified 1.4 trainer with various cheats including car unlocks. How to Use Trainer 1.4 to Unlock Everything Ensure your game is patched to v1
Start NFS Carbon and load your career profile. How to Use Trainer 1
: Unlocks the Corvette Z06 Interceptor for Quick Race. bigredfiredrive : Unlocks the Fire Truck for Quick Race. Troubleshooting Common Issues Buying new cars? - Need for Speed: Carbon - GameFAQs
This is a popular "trainer" file designed for use with Cheat Engine 6.7+ . It includes a specific "Unlock all career cars and parts" toggle and even allows you to purchase custom cars like the "Cop Z06" in career mode.