I got an ‘84 307 and when she cold starts there is weird knocking sound coming from what seems to be the back of the motor towards the firewall.

I have 40 pounds of oil pressure on start up and the sound goes away once it’s warm.

Any idea what this could be?

 

40 psi cold isn't super high. What is it warm? It might be a minor exhaust leak, flex plate bolt or a sticky lifter. A stethoscope can narrow it down.

 

We had an '84 307 brand new with a knocking noise cold. Dealer replaced the crankshaft. Transmission also failed on that car.