Although the initial landing was virtually bloodless, and you are correct in stating the major action didn't begin until the 6th of April, there was sporadic fighting for the entire Tenth Army. The Japanese employed handfuls of snipers, mortars, machine guns, etc. that fired on, and hit, Marines and soldiers between April 1 and April 6, just nothing compared to previous battles, or compared to how vicious and slow the fight would become toward the Shuri Line. From the entire Tenth Army, they suffered just over 150 casualties on the first day. But comparatively speaking, that was a negligible amount. Here is a map showing through the first few days how much ground was actually covered: https://westpoint.edu/sites/default/files/inline-images/academics/academic_departments/history/WWII%20Asia/ww2%2520asia%2520map%252048.jpg To be able to cover so much ground with so few casualties was unheard of in the Pacific, but that doesn't mean it was completely bloodless.

If you know what unit your great uncle was in, it is possible you could search After Action Reports in the National Archives and perhaps find his name mentioned, particularly since not that many were killed in the opening days.