Generally speaking, when no homing cycle exists (and therefore no homing switches)
The location the machine is powered on at, is the X0 Y0
So the “start up” location of the spindle/Laser/Head is x0 Y0
Theres a lot of nuance to this though depending on firmware settings.
On routers and specifically Mach 3 or 4 I always have -X,-Y, +Z home limit switches. -Y home comes in handy if you have two steppers and the home removes the racking or twisting that might happen in the gantry.
without a slaved Y axis I only home to get a good estimate on where some fixture is located (assuming you measured it from home in the past).
without the need for that I just jog the axis and zero the DRO’s (and don’t home the machine to limit switches) which is like resetting origin in a laser.