In order to restore your messages from Google drive, you would need access to the same number that was used with WhatsApp during the backup.
From WhatsApp's FAQ
In order to successfully restore a Google Drive backup, you need to
use the same phone number and Google account used to create the back
You can always ask the people that you chatted with, to send you a copy of the conversation by email, with the feature that WhatsApp providers for that here
Depending on how desperate you are, you can call the number that you used to use with WhatsApp, and ask the person to help you restore the chats. The person would have to send you the verification number that he receives from WhatsApp, and after you successfully set up and restore your chats, you can change your number back to the new number that you have now. (Good luck with that)