There is a provision that permits the Koninklijke Marechaussee to issue 24-hour visas at Schiphol to passengers in transit. It is purely at their discretion but if you have US permanent residency and a clean travel record you have decent chances. Go to the Marechaussee office near any of the immigration checkpoints at Schiphol and enquire there.

Alternatively, and this is a more certain option, apply for a Class B transit visa that allows you to pass through the Schengen states in transit for up to 5 days. You will then be able to exit the airside at your own will.