In the process of conducting design considerations a program's systems engineers should check?

The program's systems engineer must first check for the problem which is to be solved and possible ways to achieve them.

Explanation:

The process of conducting a design first thing would be to identify the need i.e. what problem will the design be solving.

Then identifying the target population, which is the people that will be benefiting from the design.

Next would be the design need and constraints, the need refers to what would be needed to achieve the design aim while the constraint would be the problems or hindrance to achieving the design aim.

none because it's so obvious

we need a link or picture : )