Veneziano did not play in a game in 2020 due to the cancellation of the minor league season because of the COVID-19 pandemic.

[4] Veneziano returned to action in 2021 with the Quad Cities River Bandits, making 22 starts and logging a 6–4 record and 3.75 ERA with 127 strikeouts across 93+2⁄3 innings pitched.

[5] Veneziano spent 2022 with the Double–A Northwest Arkansas Naturals, making 26 appearances (25 starts) and posting a 6–9 record and 5.72 ERA with 129 strikeouts.

[6] In 26 games (25 starts) split between the two clubs, he registered a cumulative 10–5 record and 3.55 ERA with 127 strikeouts in 132 innings pitched.

On September 19, 2023, Veneziano was selected to the 40-man roster and promoted to the major leagues for the first time.