That is not egalitarianism (which would mean something closer to everyone owning the exact same amounts), it is the standard definition of "equality of opportunity".
Where do you place the cutoff for opportunity? Are things like innate ability, motivation, interest in lucrative pursuits for their own merits, luck of the draw not also just another kind of opportunity? There is no standard because nobody can agree on a standard. The only thing we can say for certain is that the kind of society you propose will never be attained through free and democratic political processes. Make of that what you will.
There is no standard definition of "equality of opportunity"; and many definitions that are regularly-used focus primarily on an absence of unreasonable discrimination in application processes rather than fairness in the Rawlsian sense.