Ford starter relays are probably one of the most often cited modern parts that fail within a few starts, or are simply bad right out of the box.
So you can’t rule that out just yet.
Being that it’s new makes even more likely to be bad than if it was old. In fact, we usually say that getting an old tired one out of the junkyard is a better gamble than buying a brand new one over the counter.
You’ve done half the testing by jumping the starter. You now know the starter works, but if you went directly to the starter, you don’t know whether the relay is good, or the starter cable is good, or the positive battery cable is good.
So work your way up the line and jumper the starter up at the relay. If you did that already, then you have verified that the starter cable is good as well.
Next step is to jumper from one side of the starter relay to the other side of the starter relay on the big studs.
If the starter cranks, then you have verified that the battery is good, the battery cable is good, the starter cable is good, and the starter is good. Leaving only the starter relay.
So the final test (short of testing the ground as suggested) would be to jump from the battery positive to the S post.
if the starter still doesn’t crank, then you have verified that the starter relay is bad.
Or it’s not grounded properly to the body.
Do you have a main body ground? That would be a wire of at least 10 gauge from the battery negative directly to the body nearby.