Got to get a hiring manager on a team with head count to sponsor you, and its political because my manager won't want to lose his team etc. Honestly seems simpler to leave and come back.
Depending on your team/group, it can also be worth starting a conversation with your manager/HRBP about allowing SWEs in your org (vs TSCs or whatever). Other groups (GTS in GBO, for example) have done this successfully.