I drove out as far as I could (with permission) and then walked out to the edge.
I looked down into the mud and saw something that caught my attention.
It was a collapsed and broken pottery bowl. Clearly hand-worked local (red) clay with a glaze on portions.
One time over 300 years ago, when the Acadians overcame the tides and marsh, a worker was having his lunch and either forgot his bowl or dropped it.
Note that this is public land, not Parks Canada, so any such finds are the property of the finder.
I am willing to donate these pieces to an appropriate historical organization upon request.