that's not predictable, tho' I've seen plenty of parking available even on Independence Day weekend.
You can also park in the church parking lot that is one block east of the paid parking lot. They take donations for parking in their lot. It is just a short walk to the beach and there is a flashing crosswalk to cross the street.
You'd want to get about 10am to be safe. That was my experience.
No problems during the week not sure about the weekend
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We went on a Saturday late afternoon and there was plenty of parking. I don't know about early in the day.
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