McGiveron was born in Liverpool, England where he started at the youth club T.M.S, one of the top teams throughout Merseyside. He went on to impress numerous local scouts, earning trials at Liverpool, Everton and Manchester United FC academies. With all three clubs vying for his signature, McGiveron chose Liverpool FC and was at the club for six years until he decided to leave. He played than for Liverpool-based Belvedere FC, before moving on to Waddicar. Whilst playing for Waddicar, McGiveron competed in the coveted Liverpool Champion's League, a competition featuring the best teams in Merseyside. Waddicar won the title, with McGiveron being named the Jimmy Aspinall Player of the Tournament following a series of exceptional performances.
McGiveron signed for Bootle in the 2014/15 season. He started as a reserve player, and following a series of impressive performances with goals and assists, he was given a call up to the first team. On his league debut for the club, he started as a substitute against Barnoldswick Town FC. He came on after 39 minutes, with the score being 0–1 to Barnoldswick at the time. After the second half kicked off, McGiveron made it 1–1 with a 30-yard goal. Two minutes later he made it 2–1 to the Bucks with a header. He earned the man of the match award, and went on to play two more games for Bootle FC.
McGiveron then went on to sign for the Nike Academy after impressing at the Nike Most Wanted Event 2014 at St. Georges Park. He battled against 42 other footballers from around the world to earn a spot at the club. In the matches he played against high calibre opposition, including PSG U19s, Hertha Berlin U19s, Portland Timbers U23s and a host of Premier League U21s and Championship teams. His most notable performances were against AS Monaco U19s where he scored two goals in a 4–2 win. and a 2–1 away win at Brighton & Hove Albion's U21s team where he scored the winning goal. McGiveron also played in the Nike Academy's 2–1 win over FC Barcelona at Wembley Stadium on 21 November 2015 where he scored the winning goal in the last few minutes.
During the summer of 2016 he played on trial in a match for A.F.C. Liverpool. During a short time spent with the Morecambe F.C. development squad, McGiveron was offered a trial in Finland with SJK 07. After an impressive performance in a trial game McGiveron was offered a contract with the U23 squad for the 2017 season on 28 January 2017. Then plan was that he would be watched by the first team for his development and would feature in the Under 23 league games and the Suomen Cup.
