Do you have a Time Machine disk used from the Mini when it was running Mountain Lion? If so, see:
https://support.apple.com/en-us/HT201250
in the last "Learn More" section in the last bullet point.
If instead you did some type of clone backup to a disk, you can use that to boot.
If you don't have any type of backup, well, there's a lesson there but we'll skip that.
If you have access to another working Mac which either either has El Capitan as it's last supported OS or was upgraded previously to El Capitan, you can go to this link:
https://itunes.apple.com/app/os-x-el-capitan/id1147835434?mt=12
and then from there go to the App Store. I wasn't able to find El Capitan on my 2012 Mini (which supports Sierra) on the App Store. Maybe somebody knows how to do this.
When doing this, you want to make sure that you don't actually start the installation program on the computer which is downloading El Capitan. It used to be that after downloading, it waited for a little while and then did the install. I did a download on El Capitan a few months ago and there was a dialog box before installation that wasn't timed. So be warned. Once you have the installation program, you can create a bootable USB flash drive or disk.
https://support.apple.com/en-us/HT201372
If your refurbished Mini came with the install disks you can re-install, upgrade the OS so that the App Store app gets installed and go from there. (But I suspect the install disks didn't come with your machine.)
If you actually have a 2010 Mini, not the 2009 Mini, it may support Internet Recovery if the firmware update was installed.
https://support.apple.com/en-us/HT201314
Use Option-Cmd-R
EDIT: If you're using another computer which has El Capitan on it or was upgraded to El Capitan in the past, if you sign in the App Store, press the Purchased tab, El Capitan should show up there and there's a button to download it.