Alternate idea, depending on the amount of soldiers in the military base:
Start shooting them.
Ok, ok, wait. Hear me out.
You start shooting soldiers from various different buildings (using a sniper rifle, a machine gun, anything with range) and what are they going to do? They're going to have to look for you. Having to look for us means coming into the slums, a veritable maze of shacks, sewers, maintenance passages that probably have not been properly mapped in ages.
It also means interacting with the slum population. If people are really desperate, a soldier in shiny battle armour with a flashy plasma rifle would be an incredibly lucrative target for destitute people if one were caught alone. I mean sure, a soldier is probably more than a match for a single mugger, but this is the slums. Gangs run rampant in modern slums, it should be infinity worse in a dark and terrible future. Gang fights here and there, along with us shooting soldiers means that their numbers would (while probably not wiped out) start taking enough casualties that they would want to send in the heavy artillery. That means gunships, air support, etc. If a gang war tripped off between the local garrison and the people of the slums, no one would question a single ship lifting off without proper clearance. Pilots would be flying sorties day and night, and with the majority of the base's garrison fighting in a house to house, alley to alley war of attrition, sneaking in would be easy.
So the TLDR version:
Go full on ruthless psycopath mode and start a war between a bunch of gangs and the military to create a big enough distraction to steal a ship.