Is it really possible to do this on a low income?
Absolutely. Eating vegan is usually cheaper than eating the typical Amerian diet. But coming off a vegetarian diet you might be looking at spending more on some of the prepared foods. For instance, Vegan Mac and Cheese is way more expensive than Kraft's. But you shouldn't be in for any big surprises.
First off let me suggest you do a little googling. Keywords: Vegan, budget, cheap. The first 20 hits are all excellent places to start. Just pick one. Some of the articles are more like strategies (bulk food aisles, farmer's markets, batch cooking). and some are more like meal plans and recipes.
You will also see some YouTubes mixed in there. Almost every vegan Vlogger has an episode on cheap eating. They even had a bit of an internal challenge with budgets. Like a week of meals for $20 or $30 dollars. One of my favorites is the Cheap Lazy Vegan. Her whole channel is low priced and easy. (For some reason I want to call her the Cheap Easy Vegan - that sort of has a bad connotation tho. )
There are even some books on the matter. The one I can name off hand is PETA's College Handbook. I've seen it used for as little as $2.
As far as specifics go....
The more food you can make from scratch the better. If you need an appliance check the GoodWill Store first. or garage sales. But things like blenders, crock pots, food processors, pressure cookers, and woks, are going to make your life easier. but you don't have to get them all right away. Check with friends, neighbors, co-workers, and relatives. Lots of people have extra appliances they don't use in their cupboards.
The bulk food aisle is your friend. Get to know it. Not only are the prices low, the lack of packaging makes it a good environmental price. Plus you buy just what you need. You can get the same price per pound on one pound of rice - without buying the 50 pound bag. I get all my beans, rice, and oats in that aisle.
Now that it's winter and the farmer's markets are closed you will get most of your best prices on canned and frozen goods. Although you can sometimes spot a good deal on something imported. I think it was just last month that grapes from Mexico were really inexpensive. For canned foods - don't ever spend more than a buck. My local Dollar store, where everything is a dollar, sells canned foods for 79¢. The big super markets usually have at least one 10 for $10 promotion.
Tofu, plant milks, fresh green veggies, and dried fruit are about the most expensive things you should be buying. Although it might be nice for a change of pace or the convenience try to steer away from processed vegan foods (like patties, sausages etc).
I'm not sure i believe it but I read that a serving of beans and rice is about 10¢. I make a big batch of Cuban black beans and spit it up in one cup portions, and freeze it. CBB and rice is sort of a staple over here. But there are dozens of ways to make beans and rice. Same with oatmeal.