Senga was born in Gamagori, Aichi Prefecture, and began playing rubber-ball baseball as a third baseman until he graduated from middle school. The manager of the Gamagori High School baseball club saw Senga’s throwing ability and decided to switch him from third base to pitcher. Although Senga and his team never advanced to the Japanese High School Baseball Championship or Japanese High School Baseball Invitational Tournament in Koshien Stadium, Senga was recommended as a potential draft prospect by the owner of a sporting goods store in Nagoya to Kazuo Ogawa, the scout manager of the Fukuoka Softbank Hawks at the time.

On May 12, 2013, Senga earned his first pitching victory while filling in as a reliever against the Saitama Seibu Lions.[8] He tied the Pacific League record for the most consecutive no-run innings (34+1⁄3 innings) by a relief pitcher in the 2013 campaign.[9] In the MAZADA All-Star Game 2013, he made his All-Star Game debut on July 19.[10] He departed the club on September 4 due to a left flank strain, and he rested for the remainder of the season.[11] In 56.1 innings pitched, Senga had 51 games pitched, a 1-4 win-loss record, a 2.40 ERA, 17 holds, one save, and 85 strikeouts.

Senga pitched as a reliever in 2014; however, he suffered a right shoulder injury on June 15 and had to spend the remainder of the season recovering from it.[12] With 19 games pitched, a 1–1 win–loss record, a 1.99 ERA, 3 holds, and 28 strikeouts in 22.2 innings, he concluded the regular season with these numbers.