Unfortunately, it's very hard to promote anything for free. you can do some small things, but you can't expect some big results from such a cheap marketing campaign.
what you can do is create your own ANN thread, where you will present your product and in that way bring your idea closer to potential users.
Next what you can do is to run some giveaway or contest where participants will in turn get something from your project. Some NFT's gifts for example.
Hi thanks so much for your answer! Really appreciate it especially the ANN thread suggestion!
Hope I'm not being a nuisance but would you happen to have any experiences regarding to giveaway and/or reaching out to KOL? We're thinking about offering giveaway/whitelist quota to some KOLs or through partnership with some popular projects related to the game, but as a small team the only way I can think of would be to cold-email KOL or try to get in touch with those projects on discord. But then I'm not too optimistic about the possible outcome...