First attempt to reset your password at this link:
If you have already tried all of the steps at the password recovery page here then unfortunately you may not be able to recover this account unless you can remember the password or use the backup options that are showing to you.
Gmail being a free email service does not offer any support aside from what you have seen online. They simply suggest you create a new account or continue to tell you that they cannot verify the account is yours.
What you can do is create an escalation ticket and a google engineer will attempt to resolve this. Create your request here: https://support.google.com/accounts/contact/forum_ar_escalations?hl=en&vid=0-551200791626-1525369097740
If you would like to continue trying to reset the password read through my advice below.
Depending on the recovery options you set up on your account you will likely be shown some or all of the following in order to prove it is yours.
Last password you remember
Answer security questions
Enter the account creation date
Get a text via mobile phone with a code
Now let me give you some tips for a successful recovery.
The last password you remember question needs to be 100% correct or else you will fail recovery. If you are not positive on any question asked of you click try another way do not take a guess.
The security question would also need to be 100% correct.
The creation date question is very tricky since almost no one remembers. This one does not have to be 100% accurate however it needs to be close, I would guess it needs to be within a month or so but the year must be correct. Some things you can do to help you remember when you created the account are:
Finding the account creation verification e-mail which would have been sent to another account you owned at the time.
If it was created as part of a new mobile device setup, check the date on the sales receipt for the device.
If the account was created for starting mobile device service, check the start date of your mobile contract.
Asking contacts if they saved a change-of-email message sent from the new Gmail account or any other e-mail you sent when the account was new.
Checking the creation date of any other accounts opened at the same time, like: PayPal, eBay, Facebook, Amazon, etc.
If you still have access to the account (perhaps from a mobile device still signed in) check the All Mail label for the original account creation e-mail or the oldest messages you still have saved.
Now as far as the code being sent to your phone goes. If you are able to get this you should be able to recover the account. If you are still denied after getting the code you likely entered one of the other things incorrectly.
Here are some more tips of things google tracks which will help prove it is your account. When trying to reset the password always do some from a location that you have logged into the account from before and if possible from the same computer. If you try resetting the password from a computer or location that you never logged into the account from before your chances of getting back in will be reduced.
All of the above said you basically need to keep trying if you want to get back into the account and try and figure out which information you have gotten wrong.
Google leaves account security 100% up to you, the user. So if you never updated your recovery options or they are out of date for example you left a phone number or email address on the account you no longer have access to then you are out of luck with the online reset and need to use the escalation form I mentioned above.