Yes you can do it with categories.
You have only one dynamically changing page for posts. Every time you post, your home page updates. You cannot post to a page.
Pages are static, they don't change, they don't have time or date stamps, you cannot apply tags or categories to them.
Your home page (front page, blog page) changes each time you add a post. Posts have date and time stamps, and you can organize them with categories.
When you assign a category to a post, then that post can be found with a link to that category. All posts assigned that category will be found with a link to that category.
Because you can link to the list of posts assigned to a category you can also put this link (and links to other categories) into a custom navigation menu.
This way, while you are still posting to only one page, your readers can easily find posts you have made on a specific category (topic).