There actually was no Federal Income Tax until 1861, and none during peacetime until 1894. Due to how Congress' taxation powers were worded, prior to the passage of the 16th Amendment, passing constitutional income taxes was a tricky proposition.
Back then, the typical method of deriving income for the Federal government was import taxes and particularly excise taxes. Most of the taxation was on common "luxuries", like alcohol, tobacco, and sugar. These of course would be easier to collect on than an income tax, as they had to be gathered from the few producers and importers of these products, not every single citizen of the nation. Of course easier doesn't necessarily mean easy.
However, this created a situation where the US Government depended on alcohol sales to pay its bills. This was considered a big obstacle to (alcohol) Prohibition, which is a large part of what drove the passage of the 16th Amendment in 1913 and the switchover to Income taxes. Without that switch, Prohibition would have bankrupted the government.