There are a few ways to work on games with low budget, but it often creates a slower development process. It could be enough to get enough of the concept of the game ironed out to then go look for investors / do a kickstarter etc...
Game jams are a great way to get quick prototypes out of the door, and get used to designing game. The ones I prefer are the short 48h ones where you basically have 48h to create the game, and submit it. With a motivated team, there are ways of making decent prototypes for short games, or "vertical slice" (which is all the mechanics of the game, but for just a small level).
Additionally, I have considered seeking students looking for projects to work on, or motivated people that would be happpy to help create a game as a hobby.
Maybe creating challenges on forums for willing people to try a develop a part of the game, with some kind of reward for the person that created the best part, or something like that could work.
There are also longer types of "game jams", where the same project is worked on for multiple smaller jams, by different people. If you manage to motivate people to do that, and can offer perks like a place to stay for the duration of the jam, or food, or something like that, it could also work.
With a small budget like yours, finding creative ways to either create the game or generate money is a nice challenge, since going the traditional route is not possible.
I'm sure quite a few people could have interesting ideas or experience to share about creative ways of developping their projects!
For example, I am currently working on creating B2B business modeles that use my skills as a writer, game designer, concept creator, manager, tester etc... to finance the day to day expenses of my company and generate enough funds to go ask for funding from the Canadian government to create my own projetcs.