Looking to find John O'Regan from Cork to New York

[Callee24]

Hi, I am a 16-year-old student from Ireland, and I am studying my family history. I recently came across this photograph and am curious for more information on his involvement in the military and his emigration to the US. This is my great-great-granduncle, John O’Regan. He was born in 1865 in Bartlemy (formerly known as Gortroe), near Rathcormac, County Cork in Ireland and was the son of William O’Regan and Elizabeth Coleman. He went to New York with his brother Michael in maybe the late 1880s to early 1890s. His insignia appears to be from 1902 but I am not sure.

Would love to know more.