How to assign blocks to particular regions on theme install?

First of all, you should change each desired block region you want manually at Administration >Structure > Block layout Tab and then go to the config export function at:
  Administration>Configuration>Development>Configuration synchronization>Export Tab>Single item to export each the block settings for your theme.
  Then you should take a look at to the generated YAML files and placed that in a new folder within your theme at /config/install. you then uninstalled the theme and then reinstalled it as the default.

  Summary:
  1. Install MY_THEME
  2. Place the blocks in the desired regions
  3. Export config files and remove from them uuid and core config hash
  for example Site Branding block block.block.MY_THEME_branding.yml file

  langcode: en
  status: true
  dependencies:
    module:
      - system
    theme:
      - DEPENDENT_THEME
  id: MY_THEME_branding
  theme: MY_THEME
  region: site_branding
  weight: 0
  provider: null
  plugin: system_branding_block
  settings:
    id: system_branding_block
    label: 'Site branding'
    provider: system
    label_display: '0'
    use_site_logo: true
    use_site_name: true
    use_site_slogan: true
  visibility: {  }

  Place config files to MY_THEME/config/optional or MY_THEME/config/install directory (if you're absolutely sure all dependencies are met)
  Uninstall MY_THEME and clear all caches
  Reinstall MY_THEME again