This is old but in case it helps anyone else I can still get to the following URLs without having to enter billing info

https://console.cloud.google.com/apis/dashboard?project=your-project-name

If you don't know your project name try variations of the above link (shorten it a section at a time) until you see the blue banner along the top with the pull-down name of projects. If you click the pull-down you'll see a popup with all your project names which you can use to put into the above URL.

https://console.cloud.google.com/apis/library?project=your-project-name (you can get to that URL from the 'Library' menu on the left)

From here you can find and enable the API you want, e.g. https://console.cloud.google.com/apis/library/maps-backend.googleapis.com?project=your-project-name (you should see a blue 'Enable' button)

You'll probably get redirected to the billing page after enabling it but ignore that - your selected API should now be enabled and if you go back to the first URL you should see it listed at the bottom of the page (but if you click on it here you'll likely get booted to the billing page again).

https://console.cloud.google.com/apis/credentials?project=your-project-name (you can get here from the 'Credentials' menu on left)

This is where you can set up and manage your API key - there's a link at the top to 'Add credentials'. When done they will appear listed on the page and can be edited by clicking on the name of the API key in the list or the 'Actions' > 'Edit API key' triple dot on the right of the list, plus other actions you might need.

So it's possible to enable an API and create a key for it, but I don't know if it still needs billing info as I can't get it working... but that might be my limited coding skills ;)