The quickest way to verify your domain with google is to download the file provided in the steps when you verify your domain and upload it in the public_html directly on the server that hosts your domain. Have you downloaded the file? You can use FTP or cPanel to upload the file. It is only 53 bytes so it is very quick to upload. After the upload you just tick that you have dowloaded the file and uploaded the file. Google will search for the file within the server that is hosting your domain and verify your domain after that. You should be able to use Google for the service that you are registering for with them.
I hope this answers your question.