Creating static block by custom module magento2

Try this in your install/upgrade script.

<?php 

...

private $blockFactory;

public function __construct(
    \Magento\Cms\Model\BlockFactory $blockFactory
  )
{
    $this->blockFactory = $blockFactory;
}

...
...

$testBlock = [
    'title' => 'Test block title',
    'identifier' => 'test-block',
    'stores' => [0],
    'is_active' => 1,
    'content' => 'Test block content'
];
$this->blockFactory->create()->setData($testBlock)->save();

Reference