In 2003, Bush first tried gathering support for invasion in Sept 2002 at the UN. Congress granted authority for use of military force in October, and the troop build up started. Colin Powell tried one more major push for UN support in Jan 2002. The invasion was in March 2003.

That was the public facing attempts to gather support. Internally within the administration, they started working on invasion plans within a few months of 9/11. These plans continued to iterate up to being more or less locked in and approved (by Bush) in Jan 2003.