ESXi is distributed in an ISO format that is designed to install to flash memory or to a local hard drive. You can extract the files and boot by using PXE.
PXE uses Dynamic Host Configuration Protocol (DHCP) and Trivial File Transfer Protocol (TFTP) to boot an operating system over a network. PXE booting requires some network infrastructure and a machine with a PXE-capable network adapter. Most machines that can run ESXi have network adapters that can PXE boot.
The Installing ESXi Using PXE technical note explains how you can PXE boot hosts with ESXi. The technical note explains how to boot using TFTP or using a Web Server, and discusses both legacy BIOS and UEFI.