Can wires go under the supply wires in my panel?
Yes you can route the wires under the feeders there is nothing wrong with this. As far as a code reference it’s tough to find something in this case that says it is not allowed or allowed. The wires in a enclosure can even be touching the 1 requirement the insulation is rated for the voltage.  both the main and your new wires are probably rated for 600v so you will be fine.