“Staying anonymous for a reasonable time” isn’t going to be enough if your are working on a project that can possibly disrupt the world.
Check Monero's development team. They are anonymous since 2014. That means you can be anonymous as long as you are not reckless.
How long will it take for the government to come up with a hint?
Depends on your OpSec. If you use anonymous protocols like Tails, Tor and Monero, it solely depends on your potential human mistakes. For instance, if you're a tennis player in real life, well... don't ever talk about tennis from your anonymous account. If you have a real life nickname, don't ever use it online. Come up with a completely new one. Etc...