If you have a mailing list or broadcast emails to many people at once, you can take advantage of it and attract free likes to your desired blogs or social media pages. Though not related, the platforms work in such a way that they complement and build each other with time. Market your blog to your mailing lists who may not be aware of its existing by incorporating a link in the email signature. If in a company setting, let all your employees include the same to cast the net wide to reach out to many people who may be interested in that page.
At the email signature, be straight or call for action to give assurance and confidence to those who may be interested in liking the page. Say something like, “Like us on….” and you provide a link to direct that page. Such efforts done on a daily basis will get you free likes in steady numbers as time go by. Keep doing so and encourage your staff members to do the same and call for action at all instances.