You can use the Vivado Design Suite tools to add design sources to your hardware. These include the IP integrator, which simplifies the process of adding IP to your existing project and creating connections for ports (such as clock and reset).
You can accomplish all your hardware system development using the Vivado tools along with IP integrator. This includes specification of the microprocessor, peripherals, and the interconnection of these components, along with their respective detailed configuration.
The Vitis software platform is used for software development, and can be installed and used without any other AMD tools installed on the machine it is loaded. The Vitis software platform can also be used to debug software applications.
The Zynq SoC Processing System (PS) can be booted and made to run without programming the FPGA (programmable logic or PL). However, in order to use any soft IP in the fabric, or to bond out PS peripherals using EMIO, programming of the PL is required. You can program the PL in the Vitis software platform.
For more information on the embedded design process, see the Vivado Design Suite Tutorial: Embedded Processor Hardware Design (UG940).