Martinez was born in Santa Cruz, California to a Honduran father and his mother Lucila who was from Victoria, Cabañas, El Salvador.

[2] Walmer played for the Santa Cruz Breakers academy during his youth soccer and high school career.

[10] On 22 December 2021, Martinez was announced as the first-ever signing by USL Championship expansion club Monterey Bay FC.

[12] Coach Hugo Pérez had approached Martinez about playing for the El Salvador under-23 for the 2020 CONCACAF Men's Olympic Qualifying Championship in March 2021, but he was unable to obtain a passport in time.

[2] Martinez debuted with the El Salvador national football team in a 7–0 2022 FIFA World Cup qualification win over United States Virgin Islands on 5 June 2021 when he came on as a substitute.