He played college football for the Florida Atlantic Owls and signed with the Miami Dolphins as an undrafted free agent in 2018.

[5][4] Joseph played football and soccer at Donna Klein Jewish Academy in Boca Raton, Florida (and was named all-county and all-state) and high school football (in which he was named all-county, all-state, and All-America by MaxPrep.com) at American Heritage School in Delray Beach, Florida.

[4] He replaced Zane Gonzalez, who was cut from the team after missing two field goals and two extra points the previous day against the New Orleans Saints.

[20] On August 31, 2019, Joseph was released during final roster cuts after losing the kicker job to rookie Austin Seibert.

[28] In the next game against the Houston Texans, Joseph went 5-for-5 on extra points as the Titans won on the road by a score of 35–14.

[30] Joseph was waived by the Titans on September 3, 2020, after the team signed Stephen Gostkowski to assume kicking duties.

[34] During a Week 2 33–34 loss to the Arizona Cardinals, Joseph missed a game-winning 37-yard field goal attempt as time expired.

A week later, Joseph missed another game-winning field goal against the Carolina Panthers, but the Vikings would go on to win the game in overtime.

[43] On September 17, 2024, the New York Giants signed Joseph to their active roster from the Lions practice squad after Graham Gano was injured.

[44] In Week 6, versus the Cincinnati Bengals, Joseph missed 2 field goals in the fourth quarter, including one that would have kept them in the game with under a minute left in regulation, which resulted in a 17–7 loss.