The whole point of a strict lockdown would've been to nip the problem in the bud via drastic measures. Based on the experiences of other countries, it should've lasted about 3-4 weeks.
I think this idea is idealistic. It's easy to say now that we should've reacted immediately. But try just getting public support for drastic lockdown measures when the virus was new enough to have about as much impact on people's daily lives as the latest hospital bombing somewhere in Afghanistan.