If you're going to keep Secure Boot Enabled ou need to try distributions that support Secure Boot. This means that, as
@Lord Boltar sort of said, their bootloader is signed with a
trusted signature.
As the main software that provides Secure Boot support for Linux is shim, you can check which distributions are Secure Boot friendly by querying for the package shim at resources like distrowatch. If a distribution provides shim, chances are that you can boot and install it.
I wrote a piece on the whole process and how to be able to install modules on a secure boot enabled installation (it was Debian at the time of writing)
Check
https://distrowatch.com/search.php?pkg=shim&relation=lessequal&pkgver=1&distrorange=InAny to choose your distribution if you want to play along with Secure Boot.