In order to do SEO without link building, certain requirements need to be met first. For instance if you want to rank for a highly specific long tail keyword and there is minimal competition then perhaps with just on-page SEO you may easily rank.
However in a more competitive scenario (which is now most cases) backlinks may be necessary.
Be sure to use white-hat methodology when building your backlink profile. Poor backlinks can have a damaging and lasting effect on your website’s performance in the top search engines.