How much storage space does the Epic installer say it needs? Check the system requirements for the app. Keep in mind, that if you are planning on installing any other software through the Epic game launcher, that you will need even more free space for the games (many games require 10GB+ these days).
Try rebooting the laptop.
Do you have any anti-virus apps, cleaning apps, or third party security software installed that may be interfering with the normal operation of macOS? These types of apps are not needed on a Mac and usually causes more problems than they solve, plus they impact system performance. If you have any of these apps installed, then uninstall them by following the developer's instructions.
You should check with Epic for assistance including the Epic forums to see if this may be a known issue. Users on the Epic forums would be much more likely to know how to solve issues related to the Epic software as would Epic themselves.
Make sure to always have at least 20GB of free storage space available at all times for the normal operation of macOS. That 20GB of free space can disappear quite quickly while normally using macOS (not saving, downloading, or installing anything). Apps (especially browsers) can create lots of temp & cache files behind the scenes during normal use and apps may be downloading updates in the background. If you run out of free storage space on an APFS boot volume, then you won't be able to delete any files to free up space due to how the APFS file system works. Plus you may not be able to boot the Mac and you may even have trouble accessing any data on the drive.