How to trace on continuously running process?

So I wanted to know how files are opened by zsh like .xinitrc, .xprofile, .zprofile, and exactly in which order. So I have decided to strace on zsh process with the grep command to see how the open system call is called and eventually I can decide and order how these files are loaded. My command:

strace zsh | grep open

but as soon as I ran this it kept showing me the output for zsh and grep is not working. when I end the process with ctrl+d also nothing happens. So is there any way to get this grep output on this kind of process?