The indexes, and in some cases the records themselves, are on the web site of the Archives d'Etat de Genève, http://etat.geneve.ch/dt/archives/accueil.html
. Follow the links to the archives database, called Adhémar.
When you reach the database, at https://ge.ch/arvaegconsult/
, click on the tab that says "doc. en ligne", then in the drop-down menu select "Répertoires de l'état civil" and click the "Rechercher" button. The index for births 1870-1875 is on the second page. I didn't spot the entry you want, but it is possible it's there in some other form, spelling, or date. Also possible, of course, that the surname changed somewhere along the line. The birth registers for the years you mentioned are also on this site, use the "Registres de l'état civil" selection on the drop-down menu. Keep digging!
Back at the "doc. en ligne" tab, there is also a selection "Inventaires" on the drop-down menu. Among these "inventaires" or indexes, there is an index of passports issued 1815-1910.