Prosch attended UMS-Wright Preparatory School in Mobile, Alabama, where he played football as a linebacker and ran track.

He was named first-team ASWA 4A All-State selection at offensive line as a junior, as he helped lead UMS-Wright Bulldogs to the 4A AHSAA state championship, and served as team captain.

As a senior, he recorded 199 total tackles, 114 solo stops, 16 for loss, five pass breakups, and one sack, and was named first-team ASWA 4A All-State selection at linebacker and the 4A Lineman of the Year by the Alabama Sports Writers Association.

Prior to his junior season in 2012, he transferred to Auburn University to be closer to his mother, who had been diagnosed with brain cancer.

[8] On January 25, 2014, Prosch played in the Senior Bowl and was a part of the South team which included Auburn teammates Dee Ford, Chris Davis, and Sammie Coates.

On March 3, 2014, Prosch opted to participate at Auburn's pro day along with Greg Robinson, Dee Ford, Chris Davis, Tre Mason, Cody Parkey, Sammie Coates, Quan Bray, and nine other teammates.

[15][16] Prosch competed with Brad Smelley and Toben Opurum throughout training camp for the vacant starting fullback job left by the departure of Greg Jones.

Throughout the recovery process, Prosch still participated in practice and was praised by head coach Bill O'Brien for his toughness.

[18] Prosch made his professional regular season debut and first career start in the [Texans' season-opening 17–6 victory over the Washington Redskins.

On September 27, 2015, Prosch had a season-high three carries for 24 yards during the Texans' 19–9 victory over the Tampa Bay Buccaneers.

[21] With Arian Foster being injured for the majority of the season after suffering a ruptured Achilles tendon in Week 7, Prosch was the lead blocker for Alfred Blue.