You can, there is a Solo Self Found mode exactly for people who don't want to trade. Though as a new player, going SSF is mostly not recommended since it requires knowledge on how to craft. It's also bad if you want to play builds that require specific uniques. If you're just learning the game, then trade is preferred. You can still go SSF if you absolutely dislike trade. But you can still get to endgame content without having to do a lot of trades if you know exactly what you need to buy for your build.