I have some mismatched earth and natural wires on opposite sides of the main breaker box natural bars.
They are that way because the wires were short after the box was replaced with an upgrade. Can I just solder in extensions to the wires to get them to reach the correct side?

We don't solder anymore, esp large wires.

Can you provide a photo of what your working on?

There are many types of mechanical connectotrs for this purpose.