Set up apple watch without signing in to another apple ID

While I was setting up my new apple watch, I got stuck with the setting up of messages. The page prompted me to sign in with another apple id that I previously used on my phone (i do not use this apple Id any more) in order to send and receive SMS and MMS from my apple watch. However, I have forgotten the password. I tried to reset the password but I have lost access to that iCloud account, hence I'm unable to prove my identity. Is there an alternative solution (other than to wait for the period that was given to reset my password) to set up my apple watch? Thanks.