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Initial Invasion Force: In early 2003, nearly 300,000 coalition troops, including about 255,000 U.S. forces, were deployed for the initial invasion of Iraq.
https://en.wikipedia.org/wiki/2003_invasion_of_Iraq
The coalition sent 160,000 troops into Iraq during the initial invasion phase, which lasted from 19 March to 1 May.[28] About 73% or 130,000 soldiers were American, with about 45,000 British soldiers (25%), 2,000 Australian soldiers (1%), and about 200 Polish JW GROM commandos (0.1%). Thirty-six other countries were involved in its aftermath. In preparation for the invasion, 100,000 U.S. troops assembled in Kuwait by 18 February.[28] The coalition forces also received support from the Peshmerga in Iraqi Kurdistan.