Hide error message in bash

Is the error message coming from the head program (like, file not found)?

In this case you have to redirect the output from inside parens:

firs_line=$(head -n 1 file 2>/dev/null)

Moreover, you only have to redirect standard error (and not standard output which is supposed to be catched by $() to be stored in firs_line

firs_line="$([ -r file ] && head -n 1 file)"