Gmail – Can’t access the Gmail

Most likely you can't wait it out. There is a trick on android if you log in to gmail with the native mail client (or any pop3 basic client) you can bypass things like this on most mail providers.
What you can do is give them a quick phone call and have them sort it out for you pretty quickly. This is a very common problem when it comes to Google based services. People don't have the phone they set up the email with and end up getting locked out. There are plenty of options but Google has amazing live support services that could have it sorted out pretty quick. So long as you can provide the essential account information they ask for.
Remember to always keep your login recovery methods up to date and you will never run in to this problem.

Actually this (called Risk-based authentication) is a very useful verification method since it prevents your Google account from being hacked by methods like phishing, keylogging etc.

However, you can disable the feature in the Google Security Settings of your account (https://myaccount.google.com/security?pli=1#activity). When you're activating the feature "Allow less secure apps" (or something like that in English. "Weniger sichere Apps zulassen" it's called in German), then the so called Risk-based authentication method will be disabled.

But again: It's not a good idea to disable Risk-based authentication on any account. Don't forget that Google won't secure your account against phishing anymore, if RBA is disabled.