Maybe they're a patient bunch? They existed for millenia after all.
What were they waiting for?
Path to establishing a new (world) order:
1: Eliminate the old order
2: Establish the New order
3: Eliminate dissent and competing orders
If you plan is to establish a new world order, you don't sit around and wait (no matter how paranoid you are as someone else suggested) after you've completed phase 1. If you sit around and wait, especially for 200 years (how many countries that exist today are younger than 200 years? I think you'd be surprised) then you have to do Phase 1 all over again (eliminate old order).
If your plan was truly to establish a NWO then rather than do the whole vault experiment thing, you actually do "Project Safehouse" as advertised. You put 122-odd thousand of your best and brightest into your 122 standard vaults and build Vault 0 properly with correct safeguards. After a handful of years, tops, you all emerge from the vaults into a "new" nation where the old laws/constitution/etc are "Suspended for the duration of the crisis".