Thompson attended Paraclete High School in Lancaster, California. He played defensive back and wide receiver. For his career he had 152 tackles and 12 interceptions. As a receiver his senior year he set school records with 52 receptions for 953 yards and 13 touchdowns. Thompson was rated as a three-star recruit and committed to Boise State University to play college football.
After redshirting his first year at Boise State in 2011, Thompson appeared in all 13 games, with six starts, as a redshirt freshman in 2012.  For the season he had 43 tackles and three interceptions. As a sophomore in 2013, he started all 13 games and recorded 63 tackles and four interceptions.  Thompson again started all 13 games as a junior in 2014. He recorded 71 tackles and seven interceptions and was named a second team All-American by CBSSports.com.   During his senior year in 2015, Thompson tied Eric Weddle's Mountain West Conference record for career interceptions.  Later in the same season, in a game against UNLV, Thompson recorded his 19th interception of his career breaking the mark set by Weddle. 
Coming out of Boise State, Thompson was projected by the majority of analysts to be a second to fourth round draft pick. He was ranked the third best free safety and the 64th overall prospect by NFLDraftScout.com.  He was invited to the NFL Combine and completed all positional drills and the entire workout. At Boise State's Pro Day, Thompson chose to attempt to improve his 10, 20, and 40-yard dash numbers from the combine and improved on all three.
|Ht||Wt||Arm length||Hand size||40‑yd dash||10-yd split||20-yd split||20‑ss||3‑cone||Vert jump||Broad||BP||Wonderlic|
| 6 ft 2 in |
| 208 lb |
| 30 3 ⁄ 8 in |
| 9 1 ⁄ 8 in |
|4.69 s||1.66 s||2.74 s||4.33 s||7.26 s|| 32.5 in |
| 9 ft 10 in |
|12 reps||29 |
|All values from NFL Combine|
He entered training camp competing with Nat Berhe and Mykkele Thompson for the vacant starting free safety position. He was named the backup free safety to Nat Berhe to begin the regular season. In the New York Giant's season-opener, Thompson made three combined tackles in a 20–19 victory over the Dallas Cowboys. On September 18, 2016, he earned his first career start and made a season-high four solo tackles in a 16–13 win against the New Orleans Saints.  He was placed on injured reserve on November 9, 2016 after suffering a foot injury in Week 3 that eventually would require surgery.