For the Cessna 172 Skyhawk maximum glide is attained at a speed of 65 KIAS. If you're flying well above this speed, let's say 90 KIAS, and suffer an engine failure, what would be the best practice: immediately slow down in order to achieve 65 KIAS as soon as possible, or slow down slowly?
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.