According to information received, Deepika's seventh and Bombayla's eighth finishes were the best among the Indians as the men's team failed short of expectations to finish a lowly 14th in the recurve qualification rounds held Tuesday.
The women's team's second-place finish meant that the Indian women trio, with the third member being Rimil Biruly, will directly play the quarters, taking on the winners of Venezuela and Dominican Republic teams.
The women's section was topped by the Olympic team silver medallist Xu Jing (1349 points), while his teammates Cheng Ming and Fang Yuting finished fourth and sixth pushing Deepika to seventh spot with 1336.
Bombayla finished one point behind Deepika, while Rimil Biruly, overall 14th, was third best among the Indians with 1316 points as the trio totalled 3987 to finish a distant second behind China (4036).
Seasoned archer Dola Banerjee had a poor qualification round finishing 32nd with 1251 points. Atanu Das (1336) with a fifth place finish was the only brightspot among the men's as the Olympian duo of Jayanta Talukdar (1291) and Tarundeep Rai (1013) misfired.
Talukdar finished a lowly 22nd while Asian Games silver medallist Rai was last among the 65 qualifiers. India had an overall 14th place in the qualifications with the trio's total of 3640 points.
Atanu and Deepika's combined show meant that the duo finish fourth in the qualification round with a total of 2672 points giving Indians some hope of a medal.
All the finals are scheduled for June 20 and 21.