You can easily create a magento 2 search engine using expertrec for as low as 9 USD per month. Here are the steps-
- Go to https://cse.expertrec.com?platform=cse
- Enter your magento 2 wesbite URL
- Enter you magento 2 sitemap URL.
- Wait for crawl to complete.
- Add the search box code to your magento 2 website.
- Upgrade to a paid plan and take live.