Is it possible to change to a larger and type of crankset from a one-piece Ashtabula style?
One piece cranks are used on inexpensive adult bikes so larger chainrings should be available as replacement parts. The crank-chainring interface is standardized. See Sheldon Brown's page on one piece cranks.

Note that the size of the chainring will be limited by the clearance between it and the drive side chainstay.