If you stay mostly in the produce aisle of your supermarket, you're 90% of the way to being added sugar free.
Which is admittedly different than completely sugar free, since that's entirely absurd.
But we've survived every generation except the last 4 without so much processed sugar, and we now have global supply lines handing us crops practically to our doorstep.
I've actually cut out all products with added sugar (and foods that are naturally high in sugar like fruits). You need to read labels but it is not so difficult. It still leaves a pretty great variety of meats, legumes, dairy, corn, rice, and vegetables.
All you can do is attempt to minimize your intake.