Born in Chelsea, Greater London, Kilman's parents are both half-Russian and half-Ukrainian. Kilman speaks Russian in addition to English.
Club career
Kilman began his career in the academy at Fulham. As a teenager, he joined futsal club Genesis Futsal Club while continuing to play the 11-a-side game. He later joined the academy at Gillingham before signing for Maidenhead United in 2015, after making a single London Senior Cup appearance for Welling United against Cockfosters in October 2014. Kilman was loaned out to Southern Football League side Marlow for the 2016–17 season. He returned the following season and made his debut for the Magpies on the opening day of the 2017–18 season against Maidstone United, while continuing his futsal career, signing for Helvécia. He went on to make 39 appearances for Maidenhead before signing for Wolverhampton Wanderers for an undisclosed fee on transfer deadline day in August 2018. He spent the season with the club's under-23 side, helping them to win promotion from the second tier of the Premier League reserve competition. In April 2019, head coach Nuno Espírito Santo stated that "Max is 100 per cent integrated into the squad... I just see him as a very good football player, a centre-half with quality. He's big, aggressive. He has to improve like all young players, but we're really, really happy with Max." Kilman was first included in a senior matchday squad in December 2018 and was an unused substitute on five occasions before the defender made his senior debut for Wolves on 4 May 2019 when he came on as a last-minute substitute in a 1–0 win against Fulham in the Premier League. In making this bow in the Premier League, Kilman became the first player to go directly from non-League to the Premier League, with no loans in between, since Chris Smalling moved from Maidstone United to Fulham in 2008. Kilman made his full senior debut for Wolves in a 4–0 home win against FC Pyunik of Armenia in the 2019–20 UEFA Europa League Qualifying Third Round, 2nd Leg, on 15 August 2019. On 25 September 2019 Kilman made his debut appearance in the EFL Cup, playing the full 90 minutes in a 1–1 home Third Round draw with Reading that ultimately saw Wolves progress to the Fourth Round on penalties. On 24 October 2019 Kilman made his first starting appearance in the 2019–20 UEFA Europa League at the group stage, playing the full 90 minutes in a 2–1 away win at Slovan Bratislava. Kilman made his full league debut in Wolves's 1–1 home draw against Sheffield United on 1 December 2019.. Upon the restart of the Fantasy Premier League in June 2020, Kilman was considered a popular choice, through his low transfer value.
International career
Kilman made his debut for the England national futsal team as an 18 year old. He went on to accumulate 25 caps for the Three Lions. Kilman's futsal career was put on hiatus when he signed for Wolves in August 2018.