No Full Synchronisation Requirement
The easiest way to get the small amount of money you’ll need to buy your first armour upgrade the Azap Leather Spaulders, is to pickpocket the nearby citizens. Hold in the fast walk button and walk through a group to steal from them, but be sure to keep moving, as they will call for the guards and attempt to chase you down and attack you themselves. If you’re forced to fight the civilians, try to use your fists to avoid desynching from harming them.
Alternatively, you can look around for Treasures and loot them for easy money. You could also look for some of the random events around the city, such as subduing a particularly unruly drunken citizen or helping a merchant carry boxes to earn the money.