It's up to the individual manager, but most warehouses open 10-15 minutes before their stated opening time. It's a good way to get a jump on the crazy. Monday morning gets the least amount or restocking, so avoid that. Tuesday or Wednesday first thing are better bets.
Never shop on the first day of a new circular, it's a madhouse. Frequently there is a lull right before a circular begins, if nothing on your list is about to go on sale, it's a good time to shop.
There are frequently unadvertised sales, and they're on a different cycle than the circular. Check the signs for sale effective dates. Sometimes I can stock up on something perishable twice during the sale period.
Speaking of unadvertised sales, sometimes their already discounted gift cards go on flash sales. I always scan that section, and look for yell8w ink. IIRC, if a vendor goes belly-up, Costco will refund your money. In fact, most gift cards are returnable.
Costco price adjusts if anything goes on sale within 30 days. You have to take your receipt to Member Service and ask for it, but they'll make the adjustment with no hassle.
Most warehouses have self check-out lanes now. I avoid them, because the staff is much faster than I am, but the self serve option means the regular lines are markedly shorter these days.
Like
@englishteacheralex, my "home" warehouse is a Top 10 location. It's never
not busy. You definitely just have to gear up mentally for it. In my working travel days, I often shopped at other warehouses. The gas station at Gilroy (CA), never has a line, but I haven't there once a month for over a decade. Recently, we were passing through the area, returning home from a road trip. I told DH there wouldn't be a line and he was shocked when that still proved to be true. Speaking of road trips: while not conveniently close to the pumps, Costco's bathrooms are always clean and stocked.
One more oddity: Salt Lake City has a combined warehouse/business center location that is gigantic. It has things I never see elsewhere. We try to hit that one whenever we're passing through.