As of this writing, my personal website outranked a Wikipedia page for a person with the same name and finally became the first result in Google (at this moment at least). Time to sum up a couple of things I think have helped me build some online authority up to this point.
Creating content and publishing blog posts is extremely important when building your online presence. True, but that sh*t needs traction! This is where the snowball effect comes in; creating content AROUND your content. Wrote a blog post? Post a link to it on Twitter! Maybe even grab some inspiring quotes from it and post them on Instagram. Some posts are even worth turning into small podcasts. There's a huge amount of possibilities to get your content noticed. Be creative and resourceful!
Don't wait for a version 1.0 of something before putting it out there. Seriously, just don't! Got the home page of your site done? Publish it and continue to work on the rest of the pages. Your blog post still needs some tweaking? Just publish it already, and keep finetuning it once it gains some traffic. Start considering your site AND your content as an ongoing work in progress, and you'll never have to wait for that perfect moment again! Another positive side-effect to this is; you'll get used to putting out more content, and you'll get in the habit of iterating fast.
This especially goes for personal and small business sites. Start by adding your website URL to your social media profiles and other accounts that offer a public profile. Submitting your small business site to public directories (and Google My Business) can also give a huge backlink boost.
Remember that Website Checklist I published recently? I use it for every single one of my online projects, and try to tick as many boxes as possible. This has really helped me finetune my sites, and has almost become a second nature when working on something new.
If Google Search Console offers an option for something, use it! There's a TON of useful information out there, and it's all free!