Heathrow to Paddington is effectively already open (and has been for some time) - the existing service that’s branded as “TfL Rail” is the precursor to the “Elizabeth Line” branded service, using the same train and track. The same applies to Reading to Paddington.

After the Paddington to Abbey Wood service settles down most of the Heathrow and Reading services will start to run through the tunnels as well, and that becomes the full service.