We study \sim 330 massive ( M _ { * } > 10 ^ { 9.5 } M _ { \odot } ) , newborn spheroidal galaxies ( SGs ) around the epoch of peak star formation ( 1 < z < 3 ) , to explore the high-redshift origin of SGs and gain insight into when and how the old stellar populations that dominate today ’ s Universe formed . The sample is drawn from the HST/WFC3 Early-Release Science programme , which provides deep 10-filter ( 0.2 - 1.7 \mu m ) HST imaging over a third of the GOODS-South field . We find that the star formation episodes that built our SGs likely peaked in the redshift range 2 < z < 5 ( with a median of z \sim 3 ) and have decay timescales shorter than \sim 1.5 Gyr . Starburst timescales and ages show no trend with stellar mass in the range 10 ^ { 9.5 } M _ { \odot } < M _ { * } < 10 ^ { 10.5 } M _ { \odot } . However , the timescales show increased scatter towards lower values ( < 0.3 Gyr ) for M _ { * } > 10 ^ { 10.5 } M _ { \odot } , and an age trend becomes evident in this mass regime : SGs with M _ { * } > 10 ^ { 11.5 } M _ { \odot } are \sim 2 Gyrs older than their counterparts with M _ { * } < 10 ^ { 10.5 } M _ { \odot } . Nevertheless , a smooth downsizing trend with galaxy mass is not observed , and the large scatter in starburst ages indicates that SGs are not a particularly coeval population . Around half of the blue SGs appear not to drive their star formation via major mergers , and those that have experienced a recent major merger , show only modest enhancements ( \sim 40 % ) in their specific star formation rates . Our empirical study indicates that processes other than major mergers ( e.g . violent disk instability driven by cold streams and/or minor mergers ) likely play a dominant role in building SGs , and creating a significant fraction of the old stellar populations that dominate today ’ s Universe .