Did gender and class significantly influence one's life opportunities in ancient China?
The above answer deals with Confucian examinations, etc. which was practiced during the Classical Chinese period. Confucianism never appeared in China before the Period of the Warring States, and indeed was a response to that period. For that reason I respectfully believe the above answer is not responsive to the prompt.
Social and class distinction appeared early on in Chinese History. Only members of the nobility were allowed to collect taxes, which were paid by the lower classes. Only the upper classes held military or administrative positions within the government. Only the upper classes had extensive land holdings while the poor worked in the fields of the well to do. Class was determined by birth, so ones status and chances of success in life were in fact determined at birth and did not change. The upper class had a much richer and more nutritious diet (meat and game) than the lower classes; and also lived in palatial mansions made of pounded earth; whereas the poor ate only porridges and lived in below-ground dwellings.
Ancient China was a strongly patriarchal society in which men held all positions of authority. Important women in society were honored only in relation to their husbands. So strong was the patriarchal system that inheritance, which previously had been matrilineal became patrilineal. Foot binding, mentioned in the above answer, only became popular during the classical period, later than the ancient period.
It is doubtful that there has ever been a society in which gender and class did not influence one's life opportunities. Ancient China was certainly no exception. Class and gender had a tremendous impact on one's opportunities.
Take, for example, the examination system which was the only way to get into a position in the government. This was a very rigorous process that took a great deal of study to pass. People often had to take the examinations multiple times. Of course, only people of means could afford the time to do all this studying and that means that class was affecting the life chances of the people of the time.
When it comes to gender, all you need to think of is the practice of foot binding. As China became more urbanized, women's labor became much less valuable. At that point, the practice of binding women's feet began. This practice, of course, severely limited what women would be able to do. It essentially kept them confined to home. Thus, gender had a huge impact on life opportunities.