Use Gmail delegation or another "solution" like using a Google Group as a collaborative inbox.
You could try to share the 2-step verification codes through instant messaging or using a phone to confirm that the access is valid but this could open your account to risks. Also if several of you access the account at the same time this could trigger some abuse prevention/security measures, so there is no really reliable and officially supported way to do this.
It's worth to note that Google choose of words are intended to help users in a easy to understand way but this assumes that people are using their products in simple ways. On Set up mail delegation we can find
You can grant access to your Gmail account by adding a delegate. This person can read, send, and delete messages for you.
But what it actually mean is that you can grant access to your Gmail inbox. Google accounts are used to give user access to their Gmail inbox but they are intended to be used by individuals and the security measures are made in place considering this.
If Gmail delegation doesn't work for you consider to use Google Group as a collaborative inbox. Note: if don't have a G Suite account but you are open to use a @googlegroup.com email address this could be a feasible option.