Q:

Fetch fields of a block defined via content type programmatically

I've created a block type via the UI. This is a translatable block with 3 text-fields.
I am using hook_block_view_alter($build, $block) to massage the data. However, I can not seem to find the fields neither in $build or $block vars.
Any idea on the fetch the field's values programmatically?

A:

You are in the wrong entity. block is a config entity to configure where and how the block is displayed and which plugin is used to build the block.
The plugin can be a core, contrib or custom block class. In your case a core plugin, which fetches content from the database. The content is stored in the content entity block_content. 
So the entity type to modify the fields of a custom block is block_content and you have to use this hook:
hook_block_content_view_alter(&$build, $block_content)

