While replicating the entire DNA molecule does not open in one go to keep the whole molecule stabilised because it would be a highly expensive process energetically.
Actually, unwinding creates tension in the molecule as uncoiled parts start forming supercoils due to the interaction of exposed nucleotides.
Instead, helicase enzyme acts on the double strand at ori site (origin of replication) and a small stretch is unzipped. Immediately, it is held and stabilised by single strand binding proteins.
Slowly with the help of enzymes, exposed strands are copied as the point of unwinding moves ahead in both directions. It gives an appearance of Y-shaped structure which is called replication fork.