There were a few ways years and years ago before Microsoft amped up their security.
I don't think there's any ways to do it now, but if there are there's a few things you need.
First, you need to see if the account is still a Silver account. If it is, there's a chance you can try to contact Microsoft and say that it's your old account that you no longer have access to. Plenty of people vouching that works.
Recently however, Microsoft did run a purge of 1mil+ Silver accounts ranging from real names, to foods, locations, and technology.
If it's not a really common thing, you can try to see if it was purged and if no one made the account.
That's how I got my current GT.