For security reasons, we are unable to assist with account unlocks for Integrator Free orgs.
As discussed in our article here, the only option will be to sign up for a new org. We would recommend that, if you do so, you ensure you are enabling and enrolling your admin in additional authenticators (e.g. WebAuthn, Google Authenticator) so that you are not reliant on a single authenticator and add additional admins to your org that can assist with lock-out situations