Have a cab hailed and vehicle density set at 100 before starting the mission. If you see a better four door vehicle than the cab, go for it, both before or after the cutscene. Otherwise, steal the cab. If you want to steal a police car, be aware that you have to lose the wanted level for the marker to spawn at the bank. Always set vehicle density back to 1 before starting the drive. Vehicle stats chart: www.imgur.com/Gl1Dpm1.jpg

Save your ammo, ignore the cops waiting at the bank's exit since killing them doesn't speed up anything. Only kill the cop standing to the right, because he'll shoot at you in the alleyway. There are two routes that you can take after blowing up the final cop car. This video shows the right (directional) route. It's riskier because you're out in the open more, but it saves 1-2 seconds over the left route.

This video shows the left route, I recommend using it if you're worried about dying.

¤Hold W and tap Space so you jump after skipping the first cutscene inside of the bank ¤Shoot Packie twice in the chest to skip most of his dialogue after retrieving the money ¤The cops take some time to spawn in the first alleyway, as you'll see in the video ¤The final cop car won't explode if you're too close to it ¤Make sure your vehicle density is set to 1 until you're outside of the wanted area ¤Don't bother hailing the cab after getting out at Packie's house, it will despawn after the cutscene