My experience with armored vehicles is that you either hold down the A button or press up on the left joystick to get it moving.
The wartime Jeep had a turn-the-switch-and-stamp-on-the-floor-starter-button arrangement. The first ones had keys, but people kept losing them.
And when you drop that key in the middle of the desert in Afghanistan?
In Saigon, the MPs would remove the distributor caps from their jeeps when they parked them. I assume that was standard for other typed of vehicles.
When I was in the CG, all the vehicles were standard civilian vehicles with key ignitions.
When I was a kid down here in SoCal, an unemployed army vet managed to sneak into a poorly-secured motor pool and steal a tank - push-button ignition.
Now I can’t get the image out of my head of a column of tanks halting their advance and everyone gets out, turns around, and presses their key fobs and the entire column of tanks chirps cheerfully.
Yeah, but once the alarms are set and somebody walks too close to one and it barks “Step away from the vehicle”, you know it has the bite to back up its bark. 
Omg, no good responses this far in? For the record, no modern US Army tactical vehicle will use a key to START. All vehicles have some way to be secured, whether it be a cable and lock or a lock on a hatch, and yes, if the keys were not available then you were either waiting for the keys to show up or you would cut the lock.
What kind of response would qualify as a “good” response?
The tactical vehicles don’t have ignition keys part has been brought up. In tactical situations, you’re generally not locking up of vehicles which helps. As a mounted guy we didn’t just park and leave our home, storage, primary weapon in times when we might be expected to have to use them relatively quickly. The vehicle is also where the bulk of our communications were (attached to bigger power supplies and antennae so also the longer range FM systems as compared to typical manpacks). Maintaining radio watch sort of necessitated keeping someone in their vicinity constantly.
That doesn’t mean keys don’t still get lost. It just means most of the losses were outside of the time when tactical concerns you bring up mattered. The maintenance section usually kept a backup but sometimes those aren’t readily accessible or got lost too. That’s when you cut the lock. All my Company Maintenance Teams (along with company supply) had lock cutters. In addition there were a lot of tools in a mechanized unit that would put paid to a lock even if not as quickly and efficiently. Those methods were the ones usually applied 
since it was quicker to brute force with the wrong tool than get your hands on the right tool. On an M60A3 there was a trick with a helmet or hammer that could get you in specific hatch (“combat locked” with a handle/latch from the inside) on many tanks. It didn’t get the loader’s hatch, secured with a padlock, open but you could operate the tank normally otherwise. On the M1 there was no such trick to get inside. Generally for both, you didn’t lose all your keys for the platoon’s vehicles so you still had ready access to apply the three rules of tank maintenance to any lock needed. (Hit it with a hammer, hit it with a BIGGER hammer, use any other tool…as a hammer.) IME the axe was the best “hammer” to use on locks. Horrible for the cutting edge though. The wheeled tactical vehicle cable/lock system was harder since there was no convenient anvil behind it. I know of at least one case where a chunk got taken out of the relatively simple plastic steering wheel on a HMMWV. That was a bigger deal (the part was more expensive than a new lock set.) Ultimately when you’re dealing with something like a tank crew, that deals with minor fender damage using 20 pound sledge hammers and pry bars, a lock… is at best a delay.
Vehicles got dispatched to specific individuals as drivers. They had to be licensed to drive it but a license alone was not enough. There was some capacity to swap qualified drivers and just annotate it on the dispatch itself. For a bigger shift you got it redispatched through maintenance. The admin procedure could cause conflict with tactical necessity but the leadership was ultimately responsible for managing it along with managing drivers.
Not once have I ever seen a military vehicle that used an actual key to start. Every vehicle I have ever driven (HUMVEE, MRAPs, LMTVs) has an ignition switch. I’m not sure what military Monty was in, but it’s not the modern US Army.
What keys ARE used for is securing the vehicle when it’s not in use. They padlock the doors and sometimes the steering wheel to prevent an unauthorized user from pilfering it. Key control is a huge pain in the ass, for all the reasons you’d think. Theft is also not uncommon - If one soldier loses a piece of equipment he might decide it’s easier to steal from another unit than admit to losing his own gear, so securing the vehicles is important.
And soldiers are NOT all trained on every conceivable vehicle. They get trained and licensed on individual vehicles that they need to use. This isn’t GI Joe, and there’s no reason to expect some random infantryman would jump in a tank or fighter jet or something.
Abrams is push to start and that takes about 8 gallons of fuel.
Thanks that was the picture I was going to post but I got distracted.
I thought it had a pull cord, like a lawnmower.
“VIPER™ is armed”