The space shuttle main engines did fire at liftoff while the SRBs were firing. They may be a bit hard to see at launch but the exhaust mach diamonds are clearly visible e.g. in [0]. They were much more clearly visible in the 7-ish seconds before liftoff, after the SSMEs had been ignited but before the SRBs go off.
Sorry, I didn't mean to imply that the SSMEs were not firing at liftoff. Since they fire for a few seconds before the SRBs get lit, I suspect most people know what's going on with them.
