WordPress add widgets to sidebars during theme activation.

functions.php

<?php
// This codes works when theme activate.
function switch_theme(){
  $widgets = get_option( 'sidebars_widgets' );
  $widgets['home_sidebar'] = array(
    'search-1', // widgetname-1
    'text-1',
    'categories-1',
  );

  // widget = prefix

  // Modify categories widget settings.
  update_option( 'widget_categories', array( 1 => array( 'title' => 'this is custom title.', 'count' => 'on' ) ) );
  
  // Update sidebars widgets with new settings.
  update_option( 'sidebars_widgets',  $widgets );
}

add_action( 'after_switch_theme', 'switch_theme' );
?>