Born in Ormskirk, Lancashire, Dowell joined Everton’s academy at the age of 7. After progressing through the ranks and the reserve side, he signed a scholarship with the club in June 2014. He then scored in a friendly for the Everton U21 side, in a 1–0 win over Rhyl on 26 July 2014.
Dowell made his debut for the club on 11 December 2014, replacing the injured Christian Atsu 11 minutes into a UEFA Europa League group match against FC Krasnodar at Goodison Park. Everton, who had already advanced into the next round, lost 0–1. With his only first team appearances of the season, he signed his first professional contract with the club.
After being given a number 51 shirt in the 2015–16 season, Dowell, however, suffered ankle injury that saw him sidelined for two months. He scored on his return for the Everton U21 on 6 December 2015, in a 3–1 win over Liverpool U23. Dowell went on to score nine more goals for the reserve side, including a stunner against Southampton U21 and a hat-trick against Leicester City U23. On 30 April 2016, he made his Premier League debut as an 87th-minute substitute for Ross Barkley in a 2–1 home win over Bournemouth. Dowell then started the final game of the 2015–16 season against Norwich City at Goodison Park.
Two months after making his Premier League debut, Dowell signed a three-year contract with the club, keeping him until 2019. In the 2016–17 season, Dowell was a member of the Everton U23 squad to win the inaugural Premier League 2 title, in which he made the total of 22 appearances and scoring 5 times. His performance throughout April won him April’s Premier League 2 Player of the Month.