I think Bitcoin is possible without PoW; decentralized peer to peer network in which nodes verify transactions and make agreements on which transaction came fir

I think Bitcoin is possible without PoW; decentralized peer to peer network in which nodes verify transactions and make agreements on which transaction came first and then draw consensus. But then someone needs to figure out how new coins would be distributed or in another words what incentive would be to verify transactions. Btw Satoshi introduced blockchain checkpoint so no attacker can fork the existing Bitcoin chain and make a competing one.