Hi!
I applied for a firm with a rolling deadline last year on the deadline itself, and I still received a VS offer. Whilst I appreciate that rolling deadlines can make timing feel stressful (particularly when you see people being invited to the next stages), firms are still looking for quality applications throughout the cycle. A well thought-out application that clearly demonstrates motivation and understanding of the firm will generally perform much better than a rushed application that is submitted earlier just for the sake of timing.
Submitting earlier can help at some firms, but I would not panic just because they opened in October - people do still progress later in the cycle too, and they wouldn't keep it open that long if they weren't going to look at the later applications.
Best of luck!