Premises on which the Efficient Market Hypothesis is built upon
The efficient market hypothesis does not require everyone being omniscient. It works through the supply/demand and price mechanism. 

For example, imagine that you have private information that a company X is doing bad (without being a manager or other person banned from insider trading). If company X is doing bad then sooner or later it’s stock price will have to go down, so if you own it’s stock you would sell it now while the price is still high or if you don’t own the stock you would short sell it.

However, as you start selling the stock you are pushing the price down. Since it’s profitable for you to sell or short sell as long as the market price is above the actual value of the company, you would do that so much that the price would eventually be driven to the point where the price is exactly equal it’s value.

The central assumption of the efficient market hypothesis is the perfect market assumption. In a perfect market there are no transactions costs, information is costless, investors are rational. In the real world however, these assumptions do not completely hold and the market is not fully efficient. 

This being said, there is evidence that despite these imperfections markets are efficient to a certain extent as prices do adjust in response to new information. In fact it’s astonishingly hard to beat the market, and difficult to find deviations from the efficient market hypothesis empirically but now we know they exist.