This is where you use one of the backup codes you were instructed to save when you enabled 2-step verification on the account. Those codes are for exactly this sort of situation and would have you back into the account in seconds (https://support.google.com/accounts/answer/1187538). Even a backup phone number would have fixed this (it could have been a voice/land-line). Lacking backup codes, the only option is to use the account recovery form (verify your identity) to try and regain access to the account.

The only account recovery option Google provides starts at https://accounts.google.com/signin/recovery (an account can not be recovered by posting here or contacting Google). Submitting more accurate answers and using a known computer/IP-address will help. This post provides an overview of how account recovery works (you NEED to read this) https://productforums.google.com/forum/#!category-topic/gmail/SzwFXkqLvr0 and this article provides many more details on the process (you SHOULD read this) http://gmailaccountrecovery.blogspot.com/

But if you can’t correctly answer enough of the questions to prove ownership of the account Google will not give it to you.

Yes, you can.

1. Go to your account
2. Under Security (was Sign-in & security), go to Signing in to Google
3. Go to 2-Step Verification
4. Under Backup options for when your primary is unavailable
5. Click Add a phone number

To use it, when you login, click Try another way to sign in under the code box. You will be presented with a list of options where you will find the second phone number as one of them.