Nope, just the opposite. You developed an open.
That wire will never carry the load of the starter. But it was not designed to. That is what that big wire its attached to is for.
The fact that it melted, means that the big wire lost contact, and the little wire was the only ground source, so the starter load tried to go through it.
Take the big ground wire loose from where it is attached and find out why its not making good contact.
And its best if you replace the little one.
Its also possible that the big wire is solidly attached, but whatever it is attached to does not have a good connection to the stater housing.
But there is a bad connection somewhere between that wire and the starter.