Uhh it is much less suspicious for it to just be slightly delayed. Trust me.
The entire spectator system is weird and slight delays before opening a map happen in normal play all the time.
Pausing on literally every play would be extremely easy to notice and start comparing lengths (you can even internally calculate something is fucked its that blatant). The spectating client being delayed by an undermined amount of time at the start is how it will always be.