You cannot. “System process” is not a well-defined notion. “Critical to system” is not a universal, yes-or-no property.
I'm writing this post on a desktop PC. It has Apache installed, but it is not “critical to system” on this machine — I only use it occasionally to test things. On the other hand, on a public- or enterprise-facing web server, Apache would be essential. Conversely, an X server is not critical on most servers, but on a workstation, it's essential.
There is no shortcut. If you want to know whether killing a process will break anything, you need to understand what the process is doing. If you don't know what a process is doing, assume that it is critical.
“Processes that would otherwise exist on a fresh installation of the OS, and before installing any application or services” is not a well-defined concept either. Services may be critical on a particular system even if they aren't part of the default installation (e.g. Apache). Conversely, services may be included in the default installation but not be critical on a particular system (e.g. a network management service on a system with no network connection).
On Android, which is not a Linux system (it's a different system using the Linux kernel), you can call anything running off /system a “system process”. This definition is somewhat meaningful on Android, unlike Unix, because it clearly separates the base system from user-installed applications. The base system includes preinstalled apps (phone, Gmail, etc.), with a different selection depending on the phone vendor (manufacturer or network operator). A twist to this definition is that apps running off /data but for which an entry in /system/app exists are also “system” apps by this definition, just ones that have been upgraded.