Yes you can. But it would take more work and in some point you will have to start building links to keep up with competition.
If you don't want to use links, social signals may help a lot. However, from my experience, links have better effect. If your content gets shared a lot, you can rank well, but with links, you'd rank even better.
It's not one or another. Should be links + social signals + everything else that could possibly help.
With links or without, make sure you have your on-site SEO done right first.
I have read so many articles about ranking and how to rank sites and the most common advice is to build links. At the same time, I should not buy links and do comment spam. Let's say I can't build links. Can I rank my website on the first page for more competitive keywords?