Should you immediately attain max glide speed after engine failure?
According to the amplified emergency procedures of the Cessna 172 Model N POH (emphasis added):


  After an engine failure in flight, the best glide speed shown in Figure 3-1 should be established as quickly as possible.


The same POH lists 65 KIAS as the best-glide speed.

Time spent away from best glide means less glide range. If increasing time, not glide range, is your goal then the minimum sink rate speed would be what you would want to fly. In an emergency, time and glide range give you more options.

The POH and physics agree: yes, establish best-glide speed immediately after an engine failure.