I'm a senior marketer. The short answer is yes, you can market without spending. The slightly longer answer is that time is money and those forms of marketing often take lots of time, and take time away from building the product.
There's lots of free info out there, but it can be hard to separate the signal from the noise. Noise in this case often being gurus and blogs trying to get you to buy info products or make a purchase via affiliate link.
Start simple by making a site to sell your product and add a way to monetize it. Get engaged in communities that have problems your product solves. You can then reach out to people to get product feedback and maybe a sale.
But to be honest, at some point odds are you will need to spend money. If the issue is you simply cannot afford it, that's fine... bootstrap with non-paid channels.
If your issue is that you don't want to pay for anything on principle, you're going to have a rough time. There reality for most businesses is that it takes money to make money.
If you have any specific questions or want to chat, feel free to contact me via my profile. While I charge a consulting rate for hands-on work or analysis, I'm always happy to answer general marketing questions, point people in the right direction to reputable resources, etc. for free without any pressure to consult.