Cold emailing bigger blogs would be the least effective method.
Some places where you can promote your new website are, Small bloggers, Reddit, Indie Hackers.
You can try paid advertising if you can afford it.
You can write engaging Medium articles and leave a link at the end of the article to your site.
You can always do it the old fashioned way, if you can figure out where your target users are, go and physically meet them. :) The best way to promote your site.
