I built my site entirely organically but it does take time for the SEO to produce volume. Around 6 years ago my site was doing ok with around 3,000 unique visitors a day for a niche topic. I won't go into the details but my hosting company managed to have my domain delisted from Google. After switching to a new hosting company and spending time building a new site I managed to get the site added back to the Google index.How would you tackle this issue without having a budget for placing (online) ads and promote your site?
I now run at about 50k to 100k unique visitors a month (humans not bots). Everything has been done using "How to" articles designed to appeal to my target audience. I publish one of these each week and they target keywords that I find using SpyFu. I used to pay for SpyFu but found I can get everything I need with the free service.
I don't use any link building techniques, advertising, promoting on social media or guest posting. Around 80% of my traffic is search, generated by the articles I post. The rest tends to come from links, word of mouth on forums, my YouTube videos and the books I publish. Incidentally, I use the videos in the articles which tends to keep people engaged on the page.
Even after doing this, there are no guarantees. Probably 80% of my article traffic comes from less than 20% of my articles. There are a few big-hitting articles that consistently pull in the bulk of views and I will expect you to experience the same. That's why it's important to plan and identify these potential articles in advance.
If you want to try to grow organically I would recommend having an initial target of 20 keywords with reasonable search volumes (100 - 1000 searches each month but you can aim higher later). Now research the existing articles that rank for those keywords and create articles with greater value and more appeal. Publish one new article a week for the next 20 weeks. After that, find the next 20 and repeat. It's probably going to be 6-12 months for your traffic to kick in.
After 2 years, don't just publish new articles. You should be looking back through your old articles to refine and republish them. If you don't, they will probably drop in the rankings; I know mine do. It's also easier to update and republish old articles.
I'm sure there will be others on this forum who have faster/better ways, but this is what's worked for me.
By the way, I'm assuming you have the other basics in place like a well-designed site that's responsive, easy to navigate and is fast. People landing on your pages want answers fast. You need to make it easy for them. If you don't, it doesn't matter how much traffic you drive there, it won't do you any good.