How do I build authority for SEO?

I'm building a free tool site (calculators and unit convertors), which went viral in a few subreddits, sending 2K+ visitors to my site in the past few days. Its very young and most pages are yet to be indexed. I wish to turn this site into one of the most trusted and reliable sites for calculators, unit convertors and similar resources. Some things that come to my mind are fast, responsive and well designed pages and tools, better content, blog posts (maybe, not sure about this), on page and technical SEO, earning backlinks naturally and through requests. Is this approach correct or am I missing out on something? Can I beat existing competitiors which rank in google using this approach? Also, does the virality of a site on social media (especially reddit) have any effect on SEO?