Here's a sequence from before restoration of Mission Creek (September, 2013) and on through to after the first King Tide after the restoration. In the shot above, they're pulling out some of the rubble dumped on the beach in the 20th Century. You can see the pipe, 3 feet in diameter, that was the outlet of Mission Creek for decades. See how the channel traces an lazy S on its way into Budd Inlet?
With the big chunks of concrete gone, this is what the channel looked like, not long after the first shot. Rubble removal has let the channel explore a bit (see the wetted ground insiude the lower curve of the S?), but not all that much has changed.
And here we see the effects of a rainy Fall weekend. There's enough outflow from that one little pipe to flood beyond the S-channel. Maybe this is why we found a log at the south edge of the channel, a check-dam to slow the flow and keep it from eating further south. Look at the mid-range left extreme of the whitewater, and you may notice the horizontal darkness that is that log.
And here above is the outflow in January, after the channel was dug (a few meters north of the old culvert), and then "armored" with cobbles. The photo was taken a bit to the right of the above shots, but you can probably pick out the S-curved outflow channel. The momentarily exhuberant leftward spillage has subdued, and the main flow (again, as all of these shots, at a not-extremely-low tide) is still following the S, more or leSS.
Over time, perhaps, more more than less. This is the lower elevation curve of the S. See how neatly it has undercut the mantle of cobbles introduced during restoration? See the unfortunate clams, exposed to the sun by a subtle nortward migration of said S? See the subtle layers of shell hash upon fine sediment? See the barnacles colonizing what is probably only a temporary mini-cliff? Some species are surprised and maybe killed by this movement, and others take advantage.
I have no idea whether the channel will continue its slow northward migration (but I hope not, because, damn, that's a pretty beach). 150 years ago, the channel was probably north of where it is now, but 150 years ago, the southern lobe of the estuary was not buried, there was not pavement nearby, the "city" of Olympia was a minor burg (capital or no), and the Eastbay Streams (Moxlie and Indian Creeks, in today's parlance) were not themselves culvertized. Maybe Mission Creek will impose itself upon its past and future channel, or maybe not. I intend to watch (and snap shots).