Once your braces are fitted, the levelling phase begins. It ends when the teeth are largely straight and lined up in a neat row. The next phase is called the working phase. During this phase the bite is corrected and any gaps are closed. The reason the gaps don't start closing straight away is that this is done only once the archwire has reached a large enough size. Treatment starts with thin, soft archwires and progresses to thicker, stiffer ones. It usually takes at least 6 months to reach an archwire suitable for closing gaps.
This answer is for general information. Your own case needs an examination by an orthodontist.