A sandbox is created for an organization, not an individual user. When you request a sandbox we create your organisation.
In case someone in your organization already requested a sandbox, it is already approved and up and running. It will be a lot faster to ask that person to give you access than requesting a new one.
Sandboxes can be shared with users of the same organization. The sandbox requester, by default, is the "admin" of the organization. He or she can manage all roles and permissions in the portal (when logged in) under the tab “my account > settings”.