The Algiers outfit received a first round bye when the qualifying draws were made in Cairo on Thursday and will face Jamus of South Sudan or Stade Tunisien of Tunisia in a last-32 tie.
USMA, who won the African equivalent of the UEFA Europa League in 2023, were drawn against Renaissance Berkane of Morocco in the semi-finals last season.
The Berkane shirts, which had a map of Morocco including the disputed Western Sahara territory, were confiscated by custom officials when they arrived in Algeria last April for the first leg.
When the kit was not returned, the Moroccans refused to fulfil the fixture and were awarded a 3-0 victory.
USMA travelled to Morocco for the return match, but left the venue before the kick-off when they discovered Berkane would wear shirts including the map.
Berkane were awarded another 3-0 victory and then lost on away goals to Zamalek of Egypt in the two-leg final, while USMA escaped further punishment from the Confederation of African Football.
The former Spanish colony of Western Sahara is largely controlled by Morocco, but claimed by the Algeria-backed Polisario Front, which seeks independence for the phosphate-rich territory.
North African neighbours Algeria and Morocco broke off diplomatic relations in 2021 partly over the issue.
Former Confederation Cup winners USMA, Berkane, Zamalek, Stade Malien of Mali and CS Sfaxien of Tunisia are among 52 title contenders. The first round is in August and the second in September.
All five received first round byes and victory in the second round will take them into the group stage, where prize money starts with a minimum pay-out of $400,000 (370,000 euros).
Zamalek face African debutants Police from Kenya or Coffee of Ethiopia and Berkane await the winners between El Kanemi Warriors of Nigeria or Dadje of Benin.
Stade Malien take on Paynesville of Liberia or Fovu Baham of Cameroon and record three-time Confederation Cup winners Sfaxien will tackle Horseed of Somalia or Rukinzo of Burundi.
Nigerian outfit Enyimba, twice CAF Champions League winners, were another club to be given a bye and their last-32 opponents will be Hafia of Guinea or a Burkina Faso club to be named.
Zamalek, Hafia, V Club of the Democratic Republic of Congo and ASEC Mimosas of the Ivory Coast are other former African champions in the field.
