Once an individual is approved and working for a cap-exempt organization, a new cap-subject employer can file a petition for concurrent H-1B employment at any time and does not have to go through the H-1B lottery process. The employee can start working for the new H-1B cap-subject employer upon the receipt of the H-1B petition. This is called H-1B portability.
As soon as Build Fellows are approved for a cap-exempt H-1B and start their fellowship, their full-time employer (typically subject to the annual lottery) can immediately file an H-1B for them concurrently.