How do you actually test for sudden traffic spikes without spending a fortune?

Load testing always feels a bit like guessing games because synthetic traffic never really matches how actual humans behave on a live site. You can set up all the staging environments you want but real users will click things in an order you never expected and hit your endpoints all at once. I'm always curious how smaller teams handle this before pushing a major update.

Do you bother with heavy load testing tools or do you just patch things as they break on launch day?