Ron Hardin wrote:

Of course, the exhaust blowing out the front turns the turbine backwards,
and the exhaust blowing out the back turns it forwards. You're where you
started, in explaining it.

Doubtful...

The starter motor spins it in a set direction. You'd have to reverse the
polarity, if electrically driven...

The only fear is that of a "hot start" which has already be explained. Or
perhaps if you had a massive tailwind and no means of turning the plane
into the wind for startup...