Gareth Taylor’s side were clinical in attack to lay down a marker for the season in the West Midlands having narrowly missed out on a domestic double in the last campaign.
City dominated proceedings early on and it took Delap just nine minutes to open his account with his new club.
Palmer then doubled the lead on 34 minutes, with the 17-year-old looking to build upon his four goals in 11 league games last season.
Taylor's side had James Trafford to thank for keeping their lead in tact, however, with the goalkeeper making a smart save from a West Brom penalty on the stroke of half-time.
Josh Wilson-Esbrand came on for Lewis Fiorini at the break but City's dominance remained, with midfielder McAtee adding a third on the hour mark.
The advantage allowed Taylor to ring the changes, with Luke Mbete-Tabu and Timi Sobowale afforded run-outs in defence in place of CJ Egan-Riley and Sammy Robinson.
The hosts struggled to handle City's forward line and Palmer grabbed his second and City's fourth with a well-taken penalty in the 79th minute to complete the rout.
How we lined up
What it means
City make a statement with an assured performance in the season's curtain-raiser and are topped only by Liverpool, who beat Blackburn Rovers 7-1.
Next up for Taylor's side is the visit of Newcastle on Saturday, August 17.