I stumbled over the same issue, and found:
That can happen if the account was deleted. Google does not reuse/recycle old/deleted usernames.
Google do not recycle used account names - ever! This policy is strictly non-negotiable.
This is to avoid privacy issues, spamming, identity theft, confusion, etc. etc.
There are other reasons as well why some names are unavailable - profanity, misleading, pornographic , confusing, copyright, etc. Google also reserve some names.
You will need to create the account with another name
I bet this happened in your case too. Somebody else was using this name before you, and then deleted the account. Now you cannot take this name anymore, nor can you login with this email.
You have no other choice than to either take another name, or add something to your desired email address, be creative but also professional.
I bet that Google makes exceptions if it is a brand name / registered name. Then directly contact their support.