Harry Kane and Kingsley Coman then scored late in the second half to complete the rout in the first competitive fixture of the German football season.
Winners of 20 German Cups, Bayern have failed to make it past the quarter-finals of the competition since winning the treble in 2019-20.
Bayern brought in Kompany as manager in the summer after failing to win a trophy last season, their first trophyless campaign since 2012.
Bayern veteran Mueller, 34, tapped in a Joshua Kimmich pass after 12 minutes and added another shortly after, tucking in a Serge Gnabry cross.
Coman turned in a pass from new signing Michael Olise with 11 minutes remaining before Kane added another in injury time, his first German Cup goal.
Earlier on Friday, first-division sides Mainz, St Pauli and Hoffenheim each beat lower league opposition to progress past the first round of the German Cup, despite each side falling behind at some point.
Defending German Cup holders Bayer Leverkusen, who also won last year's league title, are in action in the DFL Supercup at home against Stuttgart on Saturday night.
Ulm were promoted to the second division in summer for the first time in 23 years.
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