If you're hoping to do cold applications, the primary goal should be to increase the number of companies that you find interesting/appropriate. You have to take the Long haul and track every company, not just companies that have openings for you now.
The biggest tool I use for cold starting lists is 2 identify any company who sends a speaker to a conference, that presents on a topic you enjoy. the name of that company should be tracked on a site like LinkedIn. the value in tracking the company through a site is that small companies change their names over time, medium sized companies get purchased, those tracking systems will update for you.
For every company you find, it will become easier to find more once you get past a threshold.
next is to add companies through your network, this can mean any company that has an employee from an educational institution that you came through.
I found that regional job listings, and surprisingly Craigslist, have much higher response rates and real listings then major listing sites.
Finally specialty listings are valuable as well. RemoteML and angel.co are examples of specialty sites leveraging a smaller community.
Aggregate all of this list of companies 2 a site like LinkedIn. Do this throughout your entire career without brakes.