Soeda swept past Evgeny Donskoy 6-1, 6-2 in 59 minutes. He landed just 44 percent of his first serves but still managed to win nearly three-quarters of the points on serve and didn't suffer a service break.
He also cashed in all four of his break chances against Donskoy.
Sixth-seeded Robin Haase, the only other seeded player on Monday's schedule, also didn't drop serve in a 7-5, 6-3 win over Yuki Bhambri. Haase lost just 19 points over 11 service games and saved four break points.
All four of Monday's matches were decided in straight sets.
Unseeded winners were Aljaz Bedene, who got past Joao Sousa 6-3, 6-2, and Edouard Roger-Vasselin, who defeated Andrey Kuznetsov 6-3, 6-4.