Goldberg started his career in the youth system at Bromley, where he played from every level from under–9 to under–16. In April 2010, he was offered a two-year scholarship at Charlton Athletic. In November 2011, he signed for Conference South side Bromley on work experience terms, making his senior debut in a 2–1 defeat to Boreham Wood. He spent two months with the club, making eight appearances in all competitions. After returning from Bromley, he was sent out on work experience again in February 2012, signing for Isthmian League Premier Division side Hastings United. He went on to make fourteen appearances for the club scoring four times.In the summer of 2012, he failed to earn a professional contract at Charlton after his scholarship had expired and was released by the club. In June 2012, Goldberg returned to Hastings United permanently before signing dual-registration terms with Bromley in August 2012. During his time with Hastings he was part of the side that reached the third round of the FA Cup, eventually losing 4–1 away to Middlesbrough, where he scored a long-distance goal. He finished the season as top goalscorer with seventeen goals, however, he could not save the club from relegation from the Isthmian League Premier Division. In August 2013, Goldberg signed for Football League Two side Dagenham & Redbridge on a one-year contract having impressed on trial during pre-season, scoring in wins against Whitstable Town and Dover Athletic. He was immediately loaned out to Conference South side Bromley on a season-long loan, re-uniting with his father. After an impressive start to the season he attracted interest from Football League clubs, having scored 14 goals by January. Having battled for the title throughout the season, Bromley eventually missed out on promotion in the play-offs to Ebbsfleet United. He finished the campaign with the Conference South golden boot award having scored 23 goals in 42 league appearances, and was also named the Conference South Player of the Year. The best of his goals was when he netted a screamer and then scoring a hat trick vs Chelmsford. In May 2014 upon his return to Dagenham, Goldberg signed a new one-year contract with the club having fended off interest from other clubs. In August 2014, he made his professional and Daggers debut in a 3–0 home defeat to Morecambe, replacing Ashley Hemmings as a second-half substitute. However, he struggled to establish himself in the first team and in November 2014 he joined Conference Premier side Bristol Rovers on a one-month loan deal. He made his debut in the 2–2 draw with Chester, replacing Nathan Blissett as a late substitute. In December 2014, his loan was extended for a further month, having made four appearances. He returned to Dagenham in January 2015 having made seven appearances for the club. He immediately re-joined Conference South side Bromley on loan until the end of season. In May 2015, Goldberg was released by Dagenham after two seasons due to the expiry of his contract, he made a total of seven appearances for the club. In June 2015, he re-joined Bromley, newly promoted to the National League, on a free transfer. At the end of the 2016–17 season, Goldberg left Bromley.
