Widely speaking, the three likely sources of income I can think of are
(1) People - either donations / patronage, or in return for something - you'll likely have more success with this if you provide regular benefits or at least token value in return for them.
(2) Grants from some community grant organisation, for example in Western Australia the Lotterywest lotto company gives out a large sum of grants as part of their license - but there may be other grant sources including private or government - eligibility will likely depend on your mission and actual status as a non profit and/or charity (these two things differ in Australia, no idea about other countries.. I think the US has some weird 3rd "public benefit" category)
(3) Find a home under the umbrella of some other already funded organisation that takes additional projects under it's wing, things like the Apache Software Foundation, GNU, etc. (no guarantee you'll actually get funding, but it may be possible in some cases.. some foundations may help you out legally but not with funding).
Grants are often hard work and come with various requirements, and are often even best case some chance of winning if you compete against others. And hard to maintain long term, so is more suited to short term. In most cases it is unlikely you'd get regular grants over time and there's definitely a time burn even if you can.
Some kind of patronage or regular output getting donations from people generally is easier to have recurring but actually getting a notable number of patrons/donations on a regular basis is difficult. Often not too bad once established.
Lastly a home under a foundation is likely difficult for a new project.. so in that case likely you'd need to self-fund until the point that may be possible.
Hope that helps.