On July 16, 2015, Alvarado signed with the Washington Nationals as an outfielder.[1] He made his professional debut in 2017 with the Dominican Summer League Nationals, hitting .139/.199/.228 with two home runs and nine RBI over 45 appearances. In 2018, Alvarado was converted into a pitcher.[2] He made 10 appearances for the rookie–level Gulf Coast League Nationals, struggling to a 6.59 ERA with 13 strikeouts over 13+2⁄3 innings pitched. Alvarado began 2019 with the GCL Nationals, posting a 2–2 record and 6.00 ERA with 19 strikeouts across 7 games (2 starts).[3]

On July 31, 2019, Alvarado, Aaron Fletcher, and Taylor Guilbeau were traded to the Seattle Mariners in exchange for Hunter Strickland and Roenis Elías.[4] Down the stretch, he made 6 appearances split between the rookie–level Arizona League Mariners and Single–A West Virginia Power. Alvarado did not play in a game in 2020 due to the cancellation of the minor league season because of the COVID-19 pandemic.[5]

On December 8, 2021, Alvarado was selected by the Detroit Tigers in the minor league phase of the Rule 5 draft.[7] He split 2022 between the Single–A Lakeland Flying Tigers, High–A West Michigan Whitecaps, and Double–A Erie SeaWolves, registering an 8–3 record and 2.72 ERA with 63 strikeouts and 10 saves across 58+2⁄3 innings pitched.[8]

Alvarado spent the entirety of the 2021 campaign with the Single–A Modesto Nuts. In 31 appearances, he struggled to an 0–2 record and 6.60 ERA with 33 strikeouts across 45 innings pitched.[6]