Shank somewhat resembles a drilled hole, (upper left in chart). Without seeing it clearly, difficult to confirm. If its pewter, soap and water, soft toothbrush, preserve with hairspray or water/glue mixture, (keeps it from flaking). Pewter is brittle, so be gentle. So, concave pewter button with a drilled hole shank (if it is) dates it in the 1700s. Best guess from my view. Could very well be wrong.
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Concave for sure, convex the depression is on the button face, as others have said, identifying the shank should date it. Appears to have a solid base with broken hole at the top. Leary about the 1700 range given the location you found it. If it was me, I'd do a little checking on the location, was if found in fill dirt so it might have been brought there from an older location, LA was founded in late 1700s so possible a button like that might be there, what was there before the park as well. Cool find and happy sleuthing.