While I have a hard time imagining NATO would (or could) be the true aggressor in a war with the WP, I can imagive several situations which might lead to NATO initiating hostilities with offensive action featuring an invasion of one or more WP states. Each of the situations imagine a war breaking out in the late 1970's thru early 1980s. They are not based upon the actual leadership styles in the NATO and WP states, but possible ones. Also, as others have said, the NATO force structure and logistic setup was not developed with offensive warfare in mind. Something might have to happen to make this change as well:
(1) Preventive War. Put several conservative, strongly anti-commie, nervous nellies in charge of key nations (say the US, UK, and BRD), mix in an aggressive loud-mouthed Soviet leadership, a spurt of really obnoxious DDR espionage activities in the BDR, WP military manuevers, and some sort of diplomatic or economic threats being made by the WP which could be interpreted as the lead up to an invasion of the BRD. It might not be out of the question that NATO might attempt a first strike or conventional invasion, either limited in focus to take out the DDR or the big one.
(2) Military Response to WP internal revolutions. Given another type of NATO leadership (more aggressive, mainly), together with initially "successful" revolutions in one or more WP states such as in Hungary 1956, NATO might militarily intervene, essentially daring the Soviets to stop them. I suspect this is the most likely way NATO might "invade" the WP.
One final comment: This thread has brought the revisionists out in full force. Oooh, the poor Warsaw Pact planning only for defense in depth up against evil US imperialists and their economic war machine. Quite likely NATO would have done OK against the WP if invaded, but this would have been because of individually more sophisticated equipment (especially after 1980), more realistic training in the actual theatre of action (west Germany), and better motivation, not because the USSR was preparing only for a defensive war itself.