If you find a company where you're interested in researching to eventually apply for work, here are some steps you can follow to see if any of your existing LinkedIn connections know someone at the company, or know someone who knows someone, etc.
(instructions are accurate as of late May 2022, but subject to change if LinkedIn changes their UI)
- View a LinkedIn profile of someone in your network. (eg, https://linkedin.com/in/iandouglas736)
- Near the top of their profile you should see how many connections they have (or just "500+ connections" if they have a big network). Click on that as a link. (it won't be a clickable link unless you're already connected with them)