The Pharaohs currently top Group G on six points after beating Mozambique and Guinea in their opening two encounters and will welcome Zimbabwe in Alexandria on Tuesday as they go in search of a third victory.
Despite their opponents lying five points adrift of his men, Bradley will not take the challenge lightly as they seek to extend their advantage at the top to five points.
"We've won nothing yet. After the Zimbabwe game we have two more games in June and everything could happen," the former USA coach told cafonline.com.
"But I believe winning on Tuesday will open the door for us to win this group and qualify to the final qualifying round. There are no margins for error in this match."
Egypt have not qualified for the World Cup since 1990 and Bradley admits his players would relish the chance to represent their country in Rio de Janeiro next year.
"Those players are very strong, mentally and technically. Playing in the World Cup is the ultimate dream for all of them," he added.
In the only other African World Cup qualifier on Tuesday, Algeria and Benin both have the opportunity to go top of Group H when they meet in Blida.
Benin could move a point ahead of current leaders Mali with victory, while Algeria would go top if they are successful by virtue of a better goal difference.