Hogh’s rise was gradual. After progressing through Randers’ academy, an injury-disrupted spell led to a move to second-tier Hobro, including a loan stint at Icelandic side Valur.
He joined Danish Superliga club AaB in January 2022, but moved again a year later to newly promoted Norwegian Eliteserien side Stabaek.
His breakthrough came there: six months into a year-long loan, Stabaek triggered their purchase option after he scored eight times in 14 matches.
Three months later, he signed a pre-contract with Bodø/Glimt to join their top-flight rivals in January 2024.
He finished as his new club’s leading scorer with 12 goals as they retained the Norwegian title, and his seven Europa League strikes made him the competition’s joint top scorer as they reached the semi-finals.
In 2025 he again topped the club’s scoring charts with 17 goals, though Bodo/Glimt ended second, a point behind Viking.
In January, he netted a brace in a 3–1 Champions League win over Manchester City and scored again the following week in a 2–1 victory away to Atletico Madrid.
Hogh received his first Denmark senior call-up in March and debuted as a late substitute in a 4–0 win against North Macedonia.
In his second outing, he came off the bench to head Denmark’s equaliser in the World Cup play-off final against the Czech Republic, only for his side to lose on penalties.