The hosts lost 12-0 to Bundesliga champions Bayern Munich at this stage of the competition last season, so they will desperately be hoping to keep the scoreline much closer on this occasion.
Match preview
Despite that heavy defeat to a size which completely dwarves their budget, though, Bremer achieved their primary aim of gaining promotion to the fourth tier of German football last season by winning the Oberliga Bremen division.
Benjamin Eta's side won the division in some style, too, remaining unbeaten throughout the entire league season with 98 points from 34 matches, scoring 152 goals in the process.
Yet, given that they have failed to score in each of their last six DFB-Pokal matches, even bagging one goal on Sunday against Schalke may well be celebrated more than any of those 152 last season.
Indeed, Bremer have not progressed beyond the first round of the DFB-Pokal since losing 3-0 to St Pauli in the second round in the 1986-87 season, so they will be sure to give it their all despite the odds being stacked against them.
After all, Schalke are a Bundesliga outfit once again having won 2. Bundesliga last season, finishing two points clear of title rivals Werder Bremen to be promoted as champions.
Winning more often than not should go a long way to helping Schalke fans move on from the 2020-21 campaign, which was a deeply forgettable one for Die Konigsblauen as they were relegated from the Bundesliga for the first time since 1991, and with a record low points total and record winless run to boot.
Former Arminia Bielefeld boss Frank Kramer has taken the reins for the forthcoming season, with avoiding relegation set to be his primary focus.
Pre-season has been a fairly negative affair, though, with two wins over relative minnows punctuated by draws to Salernitana and Augsburg, as well as defeats to SV Meppen and FC Twente. The 50-year-old will be keen to avoid any embarrassment in Bremer on Sunday ahead of next weekend's Bundesliga opening clash away to FC Koln.
Schalke 04 pre-season form:
Team News
Bremer appear to have no major injury concerns ahead of Sunday's cup tie, boosting their chances of carrying out a major upset.
One of the players who featured in early June's 3-1 over FC Concordia Wilhelmsruh have since left the club, with new signing Dylan Burke likely to replace him.
Schalke, meanwhile, will travel without defender Malick Thiaw due to suspension.
Despite losing 3-1 to Twente, Kramer may trust the same XI to perform closer to his high expectations.
That would mean competitive debuts for Thomas Ouwejan, Rodrigo Zalazar, Sebastian Polter, Tobias Mohr, Tom Krauss, Alexander Schwolow, Cedric Brunner and Maya Yoshida in what has been an incredibly busy summer for the newly promoted side.
Bremer SV possible starting lineup:
Seemann; Warm, Nobile, Burke, Kmiec; Muszong, Kaiser; Kurkiewicz, Arnhold, M Diop; L Diop
Schalke 04 possible starting lineup:
Schwolow; Brunner, Yoshida, Kaminski, Ouwejan; Zalazar, Latza, Krauss, Mohr; Polter, Terodde
We say: Bremer SV 0-2 Schalke 04
We expect Bremer's goalless run in the DFB-Pokal to continue, but Schalke may make harder work of their first round tie than expected.
With so many new players to integrate into the team, Kramer and the Schalke fanbase alike may have to be patient before expecting instant results this season.