There are several ways to get that, the most common is via routing rules.
Define your routing rules to assign tickets to Level 2 based on well-defined categories (the third level category is often used to specify what services are handled by Level 2 or above). Make those categories visible (and hide other ones) to Level 1.
In order to assign the tickets, Level 1 has to change the category so it's SysAid which routes tickets to Level 2. Enable the related permission under Settings > Service Desk > General and make Admin Group field in read-only mode for Level 1 group only.