I’m sorry to say that putting a website online is not as simple as uploading it to a server and leaving it there untouched forever. Technology is constantly changing and your site will require updates. If you are using an out-of-the-box site creator, these will be handled for you. But if you are using a CMS, these will need to be done yourself.
Additionally, there could be other problems with your site, unrelated to out of date plugins or themes or code. There could be errors missed when uploading the site, or unforeseen issues that pop up.
The long and the short of it is, you need to be able to diagnose problems on your website whenever you have the time to check. How do you do that?
Checking for Updates
If you are using a CMS (Drupal, Joomla, WordPress), your CMS will tell you about updates when you login to your website. Even if you are never going to add new content, it is a good idea for you or your website to periodically long in to your site to see if there are updates. I’d recommend once a week, at minimum.
If you are using an out-of-the-box site creator most mandatory updates should be handled for you by the service you are using.
If you have a custom built site you will unfortunately need a webmaster on call to discover what you need updated and when. Once again, a custom site is a terrible idea.
Checking for Problems
There are other problems that will arise over the life of your website. Fortunately, most of them that will impact how potential customers find you can be found using Google Search Console (formerly Webmaster Tools). I did a presentation on how to set up a Search Console account in 2017. Using Search Console, you should be able to discover most problems which will affect how people find your website through search engines.
Unfortunately, for typos, you’ll just have to read your site content (or have someone else do it).