The main time consumer is the beans. If you're making your own beans, it takes about 2 hours to cook them. If you're using canned beans and ground beef, you can cut a lot of time off. However, chili does need time for the flavors to build, meld and even cure. You also get the benefit of intensified flavors through some reduction. It's usually better the second day so you might consider making it quickly the day before and keeping it overnight in the refrigerator.
I make my own beans in a pressure cooker. No need to pre-soak and they finish in about 45 minutes. During that time, i can chop the vegies, cube the meat, do the cooking and combine them at about the time beans are done. Doing my own beans gives me a chance to add more flavor to the beans as they cook, usually some onion, garlic, bacon fat and so on.
So off the top of my head, if I had to do a rush job on chili with ground beef and canned beans, I'd probably do something along these lines.
2-3 tablespoons bacon fat
about 2 tablespoons chili powder -- This will vary to taste and brand of chili powder as they're all different. be prepared to add more to taste during cooking or cut down on some ingredients later on which I will point out.
1 pound lean ground beef I want to add flavor with the fat so I used bacon fat but want maximum beef in the dish without it rendering away during cooking.
1 large onion chopped to your texture preference. I prefer a small dice.
2 roasted red peppers from a jar chopped medium to fine
4 large cloves garlic minced
1/2 teaspoon ground cumin -- this is one of those ingredients you might adjust up or down depending on your chili powder. But this is probably close for most chili powder brands
1/2 teaspoon oregano, mexican preferred This too is a staple ingredient of chili powder and may be adjusted up or down to taste
pinch ground coriander -- just a warmed citrus flavor of the borderlands I like so consider it optional
28 oz can crushed tomatoes
15 oz can of beans rinsed and drained I'd choose a canned pinto or small red bean.
beer or water to adjust texture
salt and pepper to taste
corn masa mixed with water in a slurry for a little flavor and thickening.
Do not use a non-stick skillet. You want good browning and fond development in this dish.
Heat a large skillet over medium heat. Add the bacon fat. When the bacon fat melts, add the chili powder and stir to mix. When it becomes aromatic in 30-60 seconds, raise the heat to medium high and add the ground beef. Stir to break up the beef and season with salt and pepper. Continue stirring occasionally until well browned. Remove from the pan leaving any grease behind. Put the ground beef in the pot you'll be making the rest of the chili in.
Add more fat/grease/oil as needed to bring the amount up to about a tablespoon. Add the onions and roasted pepper. Season with some salt and pepper. Stir to remove the browned bits from the pan. Stir frequently. The vegetables will release their juices helping you incorporate the fond into the vegetables.
When the onions are tender, about 6 minutes, add the garlic, cumin, oregano and coriander. Stir to mix and frequently thereafter until quite fragrant, about 1 minute. Add the vegetable mix to the chili pot with the beef.
Rinse the pan with a little water or beer to get all the last bits of vegetables, fond and flavor. Pour it into the pot with the rest. Start heating the pot over medium heat.
Add the tomatos and beans to the pot and stir to mix. Adjust texture as needed with water or beer. Let simmer at least 1/2 hour. An hour would be better still but you're in a rush. At the end, mix a slurry of 1 tablespoon corn masa with 2-3 tablespoon water. Pour it in and stir. Taste, correct seasonings.
If you add more chili powder or spices at this point, you should let them cook a bit, say at least 10 minutes before tasting again so they have time to do their thing.
This will be mild as I've not added much for heat. I've no way of knowing your heat preference or to whom you'll be serving it. You can add pure ground chile powder (california or new mexico are easy to find and mild to medium heat) Add that with the spices for the vegetables. Or use hotter peppers in place of the roasted reds.