Possible? Yes. Easy? No.
Look, most non corrosive primers use lead sthyphanate as the explosive, so you are almost NOT going to get away from all lead.
Beyond that, how silly do you wish to be? I think Guns Magazine had an article many many years ago by some person loading wooden bullets (for vampires, of course) and with light charges of powder, they went down range and hit the target... No uncommon in training ammo. Swede 6.5 is currently available per lists. Germans loaded wood bullets in WW II.
Many years ago, man, gunsmith, friend told me that there was a common zinc alloy, Zymac, that was used for grills and the like in autos (before plastic took over) and you could melt it and cast it with the better, more powderful lead bullet furnaces and molds. Never got around to trying it.
You mention costs. Get real. Lead has been in use for centuries. It is the standard. Going some other way is going to cost more just because of the lesser demand.
Mr. Corbin, Dave (corbins.com) has the technology worked out to make bullets with either tungsten powder (heavier than lead) or copper powder... In a copper jacket is easier. You can heat the copper swaged bullets to get the grains to "melt" together and become a unit...
So, the options are out there. For standard performance, you use lead bullets. For other options, you do your own homework and see what suits you. luck.