When you are on the CM.com homepage you first have to Sign in, into your CM.com account. This is accessible by pressing on the Sign in button on top right side. You'll get navigated to the Sign in page, here you can sign in with your CM.com account.
You can find the Customer Data Platform on the CM.com Platform. Click on the nine dots and select the Data app.
Do you get an error message? Or you cannot find the app in the App Center? Then contact your CM onboarding manager.