To create a fully-featured site via REST or to implement updates to an existing site, please take note that REST copies the logic of user behaviour. First you have to add a block, before modifying it (if it wasn't previously added to a page). For modifications to be visible, this page must be published.
Let's go down the list of necessary action items:
- Create a new site or select an existing one. You will have a site ID available for further use. (Methods to handle sites.)
- Next, the landing page. Create a landing page in the same manner or select an existing page. (Methods to handle landing page)
- Blocks. Blocks are molecules of sites (nodes are atoms). You should have a good understanding what a block is, and what is its manifest. You can work with blocks within a page (add, move, delete) via these methods. You can also work with a specific block via these methods.
- Don't forget, after all manipulations, the landing page must be published.
- If you do have enough blocks, you always can register new ones.
These steps are minimal requirements to start handling blocks. Certainly, there are many more other methods and they are appropriately specific to cover the maximum of your individual cases.