In addition to what Stephen and Closetnoc already said... There is no magic bullet here, and definitely no guarantees. Here's what you're up against, and what you can do to improve your chances. (And it's not just luck, it's skill and strategy too!)
Several years ago, when every marketing consultant ran around and charged $150/hr to say "content is king, create more content," a lot of brands started to crank out massive amounts of content, expecting every blog post and tweet to bring massive results. They used keywords, they produced both high quality content and link bait, they occupied every social media channel regardless of whether their audience was on it. (Financial journalism Pinterest boards, I'm looking at you.) When that didn't bring about the desired results, many abandoned this tactic within a year or two. That's why there are no guarantees, even for rich corporate entities.
Depending on your site and content, you may be up against some corporate entities, who have SEO teams and advertising dollars and industry clout.
Your site is brand new. It hasn't earned the trust of search engines. It probably has a small footprint, for now. Until it ramps, which can take a while, your natural link building may be hampered by the fact that you don't have much of a history in SERPs, or that you don't have a lot of trustworthy links. (I know - you need links to earn more links - sounds tedious, but there it is.)
What you can do:
Don't just focus on keywords; work with trends. One of my clients earned her most successful blog post (for a fashion blog) when she wrote about Michael Jackson, and he died the next day and became a trending topic just after her post went live.
Don't forget technical SEO. Without things like good site speed, structured data, metadata, Search Console work, etc., your content has far less of a chance to climb the SERPs or be found at all.
Consider some paid advertising, whether on AdWords/Bing or social media. The giants can afford to do this, and are doing this. You targeting would have to be more precise, therefore; more niche. At least at first, you can drive people to your content that way.
As the others have said, maximize your free social media presence. That said, the reach of free Facebook pages is slowly decreasing, as there is more noise now, and social media companies try to drive brands to their ad product.
Finally, even if you don't reach out for links, you may have to engage with other webmasters as they reach out to you. Also, I'd be remiss not to mention the fact that link building can be effective; if you write a positive restaurant review, for example, why not tell them about it? They may post it to their social media or blog. That's how discovery happens, and this can be much more effective than an ad or whatnot.
Again, no guarantees here, but you seem determined to make your site succeed, and you are hopefully passionate about the content you will create. Good luck!