This page of the guide to Mafia Definitive Edition contains a walkthrough for the main mission 1 – An Offer You Can't Refuse. Our solution tells how to lose the pursuit and how to escape the gangsters, as well as how to get to Salieri's bar safely.
The mission begins immediately with a chase scene – you have to escape hostile gangsters. Tommy can't shoot. Focus on flawless driving, i.e. avoid collisions with civilian cars, pedestrians, streetlights, and other large objects. You don't have to follow any fixed route, although try to choose longer straight roads to keep the speed.
Locations marked with arrows will help you lose your chase. You can come across them while driving. They are also visible on the mini-map and on the city map, which you can see by pressing the right key.
Reaching each location with arrows will trigger a short scene - Tommy's taxi will automatically omit the obstacles. One of the enemy cars will crash. Use this tactic to easily get rid of more enemy vehicles. However, you have to avoid going back to the same location marked with an arrow a second time. Always drive to a new area.
Reach the Giuliani Bridge
After losing the gangsters, start moving towards the Giuliani Bridge. It is best to follow the optimal route marked on the mini-map. Using the bridge will allow you to reach the Central Island district. New enemy vehicles will appear.
Escape the gangsters
Several gangsters' vehicles block the bridge. The solution to this problem is simple – press the ramming button to get through the blockade.
You have to lose another chase. Just like before, find places marked with arrows on the map. In each of them, you can crash one mobster vehicle. Keep reaching these locations until all enemy cars are destroyed.
Reach Little Italy
As you travel to Little Italy, pay attention to the red icons of the vehicles on the mini-map - these are gangsters patrolling the area. Stay away from them, otherwise, a new pursuit will start.
During the ride, you must cross a partially raised drawbridge. It's not difficult – just try not to drive too slowly. Watch a cut-scene showing a jump to the other side of the river. Finish the drive to Salieri's Bar, where you don't break traffic rules so you don't get caught by the police. Reach the bar and then watch a cut-scene ending the mission.