In every war, each party has a goal:
Marine's was to execute Ace publicly.
Whitebeard's was to rescue Ace.
Of course they were trying, but they weren't on the offensive. Whitebeard was. That's why the Admirals only made their moves after WB's first earthquake. WB even tried to talk to Sengoku before starting the battle.
The Marines were not trying to kill WB nor his allies. Sengoku even allowed Garp to not join the battle until the pirates started taking advantage on the war. Those who were going all out were the pirates, since they had to beat the greatest military force in the world; the Marines were just protecting the island and keeping the pirates away from the platform.