If you’re in the Columbia River estuary, i.e. the lower 25 miles of the Columbia River near Astoria, then there is no best time, the sturgeon are always on the bite (during June and July) but the incoming tide may definitely have an advantage over the outgoing tide.
When fishing outside of the estuary you will find that sturgeon show a strong preference toward feeding heavily in the morning and then tapering off significantly after late morning to early afternoon. Most days the bite will drop off sometime between 10:30 and 1:00.
What do you do now? You can stay in the spot where you’ve been catching them because you know you’re in a good location, you will definitely catch an occasional fish, or you can move to another good location where you know the fish haven’t been bothered that day.
If it’s this late in the day and you’re in a good spot, catching fish (albeit a reduced number since the morning) and you don’t have a “go-to” spot in mind, then I would stay put and not go prospecting. Moving around during the afternoon can be pretty fruitless because the sturgeon are already full and they don’t bite well. However if you weren’t into the fish in the morning, you don’t have anything to loose and you better get moving!