Blocking Titan's door will completely skip the entry animation, you can see demonstration of this in my 3:05 solo A Titan of a Job run (timestamped link):
Missions limiting your spawn point away from certain objectives can be bypassed by using a garage/property as demonstrated in our 2:37 Base Invaders run:
Adding to the last one, if you start a mission inside a property, fail it and use 'Replay' button (haven't tested Quick restart), it will ALWAYS start it inside the property you first started it in (normally it'd teleport you to the set spawn location for that mission). This will persist until you completely exit to freeroam and start again.
While getting on Oppressor MKII, hold (RT on Xbox, R1 on PS, and W on PC) and continuously spam (RB on Xbox, R1 on PS, and Space Bar on PC) and (A on Xbox, Square on PS, and X on PC) while (holding back the analog stick on Xbox and PS and S on PC) and your Oppressor will be launched upward.
There are probably a few different situations where this would be helpful (i.e. when there is a building/cars/obstacles in front of you).