No. You don't need a google account while setting up your new android phone. It is possible to skip the now option while setting up a process to avoid creating or providing a google account. It doesn't have any impact on apps like contacts, or messages. But while using your phone for some proprietary applications google account is a must to have. To sign in to other third-party app applications or avail of the best services of these apps it is required to have a google account.