‘Now after (or ‘late on') the sabbath day, as it began to dawn toward the first day of the week, came Mary Magdalene and the other Mary to see the sepulchre.'
The women disciples had to wait until the Sabbath was over, because by Jewish Law they could not anoint the body of Jesus on the Sabbath. And while the other women were finalising their preparations the two Marys were sent on towards dawn in order to survey the situation and to consider the possibility of the removal of the great stone blocking the entrance to the tomb. The others would follow on more slowly. Matthew as usual abbreviates what happens, and opens with the arrival of the two women at the tomb.
The word translated ‘after' can signify either that or ‘late on'. Here it must mean ‘after', as the Sabbath had ended on the previous evening.