cat じゃなくて tail でやればよい。
$ tail -n+1 test* ==> test <== 123 ==> test2 <== test
man tail . . . Numbers having a leading plus (`+') sign are relative to the beginning of the input, for example, ``-c +2'' starts the display at the second byte of the input. . . .
cat も tail も語彙が猫っぽい。
参考: bash – Force newlines with cat wildcard printing – Unix & Linux Stack Exchange