U can probably find a camp sight at big meadows that time of year , its off season . If not lewis mountain isnt far and they will have spots as well. Its the off season so you should not have any trouble.
I would call and make a reservation just to be on the safe side. This is a fairly large campground, but it's not unusual for it to fill to capacity on weekends.
You can check to see if any reservable sites are available on Recreation.gov. If they're all booked for that day, then there's a good chance you won't get a site when you arrive that late (they do have some sites available for people who just walk in). But since school is starting this week, you might be fortunate to find a site. You can always call the campground to get their advice. Big Meadows is one the most popular so you could fare better at other campgrounds.
I'd call the office...they are pretty knowledgeable with the web and flow...when we went on August 10th we got one of the last 2 and we were there by 11 but you might be going on a less crowded weekend
Thanks! Your answer is awaiting moderation.