The 129th IR was part of the 37th ID, which shipped out for the South Pacific 26 May 1942. He was detached from the prior to this for any number of reasons. My initial suspicions was the he may have been part of the cadre that formed the 99th, but they were already in the ETO, on the line when arrived there, so I don't think that is correct. What he was doing during the intervening time, who know? He could have been detailed training new men, been part of the
ASTP program, any number of things.
Could he have landed on the 9th and be with the division on the 16th? Yes. That is a week and certainly not a short period of time for him to travel a few hundred miles.
Are you sure of the unit designations in your first post? Disregard the First Army, that was not a static formation. I am finding other pages that say he was in the 83rd Infantry Division and the 83rd ID crossed the Wesel very close to the time frame he was wounded. The infantry regiments of the 83rd were the 329th, 330th & 331st, not the 395th