Scientists and the government do willingly lie though? And a proper science education will have you go through the math and do experiments yourself so you don't

Scientists and the government do willingly lie though? And a proper science education will have you go through the math and do experiments yourself so you don't need to believe it (well, you need to believe you are not being tricked by a Cartesian demon). If you're not doing that, then yeah all you have to go on is credibility of the people doing science, and several fields have replication crises, so it makes sense to not blindly believe them.