I think that the answer to this is going to depend on how one views the role of the state. Some, such as the Classical Liberals, believe that the state must do its part to stay out of the affairs of the marketplace and allow it to function to its natural end. In this light, freedom is secondary to the results of establishing anything artificially challenging the pristine nature of the marketplace. This non- interventionist approach is challenged by those who believe that government should take an active and strong role in ensuring that all of its citizens are guaranteed the same opportunities. In this light, government commits the sin of silence by not ensuring a sense of equality for all of its citizens.
There are financial and practical limits, as suggested above, but there is so much more government can do to create equality of opportunity that would, in my opinion, greatly improve our society.
In some democracies in Western Europe, and indeed, in many countries around the developed world, college is paid for by the state, and in full. This means from a very young age, everyone has the ability to attend university regardless of financial status. This means students could take more challenging classes, and would conceivably work harder to preapre themselves. The whole education system is improved in one fell swoop.
What's more, most economists will tell you that it's cost effective to do this, as college graduates earn much, much more over a lifetime, and therefore pay more in taxes on those earnings, essentially paying back government and society for the initial investment.
I would say that the state should go as far as possible. Of course, that has to be balanced against what we can plausibly afford to do. So I have no specific answer except that we should do as much as we can possibly afford.
Sadly, the state cannot go as far as we would like. It cannot afford to send a tutor to the home of each "at risk" kid to help them with their homework the way some kids' parents can help them. The state cannot afford to make every school have equipment as good as those in the richest areas. So we can't really do as much as we should.
But we should do everything we can to create this because it does not seem fair to have some people have fewer opportunities just because they were born poor.
Talking about USA, the legal framework of the country already provides for reasonable degree of equality of opportunity for all people. In general the country follows a model for market driven economics that provides equal opportunity for all. In addition there are specific laws to protect the interest of the weaker people and to control aberrations in the social system due to historical prejudices. For example there are specific laws to control monopolies that harm general interest of public. Similarly there are laws that create transparency in working of big corporation and institutions such as stock market to safeguard interests of individual investors and consumers. Many consumer protection laws also exist to ensure that large corporations do not indulge in unfair market practices. The concern for equal opportunity is specifically addressed in laws against discrimination of all kinds including the ones based on gender, race, and religion.
The government of every country needs to get actively involved in assuring equality of opportunity to all its people. The approach adapted by USA in this matter appears to be quite effective. I would say that most of the other countries also will need similar levels of government involvement for this purpose.