How is Rand's "liberty" supposed to be provided?
It seems to me we already live in a universe where people have as much free will as we ever will. Some people use this free will to restrict the free will of others. Sometimes this is a government, sometimes it's a corporation, or sometimes it's a kidnapper.
But what hypothetical external agent could ever ensure that no one's free will will be restricted? To have such a system would necessitate restricting people's free will so that they couldn't restrict each other's free will; it would be a self-defeating situation.
This is analogous to the set of all sets in mathematics, or other paradoxes that arise by having "all powerful" objects. Humans are so free, that we are free to kill ourselves (for instance), and remove our freedom. Likewise, we are free to disable our own free will.
How could Rand change things so that this is not the case?
In my view, governments are the result of the utter freedom we have as humans. It is simply absurd to think of getting rid of the systems that restrict freedom; if we did, the freedoms granted would simply create new systems, like corporations, or another government, that would replace all the functions of the system we got rid of.
Let me put it another way: It seems we already have maximal liberty. How are things ever going to be better in that respect?