Lots of small business can make a profit on their first day of trading. Lots of small businesses can take weeks, months or years to turn a profit. It depends on the business.
For example, you can rent a market stall for a day. First thing in the morning on day one, you go to the wholesalers and get a trolley full of goods. Drive it to the market. Assuming you've picked the right products, the right market and are selling at the right price, it would be very difficult not to turn a profit on your first day. (However, if you needed to buy a van to move your goods, that's a different matter!)
It's not really helpful to make sweeping statements as to timescales when a business moves into profits. It gives people the wrong sense of security if they're still loss making after 2 years but are led to believe that's normal when it's the type of business that should easily be profitable after 3 months!
What matters more, is the direction of travel, i.e. are customer numbers increasing, are sales values increasing, are profit margins healthy, are costs under control. With that kind of information, you can extrapolate the next couple of years to see when and if you will turn into profits, and then you can make an informed decision as to whether to wait it out or give up or change direction.