They don’t actually know. If they think something looks suspicious, they do an audit, and then they know.
The vast majority of people’s taxes fillings are taken on good faith.
They don’t actually know the final amount, but they do have an independent expectation for certain items.
If your job withholds income tax then it is paid quarterly to the government, so they know how much you made and how much taxes you should be paying.
If you win a large sum of money in the stock market or gambling at a casino then the broker or management company reports a tax bill to the IRS. The same happens for large early withdrawals of retirement funds.
They also know information based on previous returns, like how many kids you have or if you own a home.
They may not know it down to the dollar amount you’ll be paying because of the complexity of the US tax code and the deductions you’ll claim. For example, the government has no record of you purchasing a $600 electric car charger but you can claim that on your taxes to reduce your tax liability. That being said, if you under-report the amount you made at your job they will almost surely audit you if the number reported by your employer doesn’t match the number you provide.
In many countries, the government does have a record of you purchasing that electric car charger as long as you ask the seller to include your tax number in the receipt - which you need to do if you want to file it - and it all comes automatically pre-filled in my tax deductions. Its become really easy to do taxes, it’s literally 3 clicks for most people.
