If I had the budget, I would improve my garden pond to have a pumped natural bog filter. Unfortunately those can take up near 2x the area of the pond itself!
I follow a group that is enthusiastic about natural swim ponds, and many of them are amazing, but well outside of what I am willing to spend.
Either way, I would still emphasize to consider a rubber liner for a pond that size. You will be sadder for the initial investment cost, but happier long term.

But hey, try and excavate a test hole and see what you have to work with. Maybe some nice clay, or maybe sand and gravel down to bedrock.

Good luck!