If it starts up after its initial burp, it's likely not the TFI then.
On the grey ones, there's a terminal that differentiates starting vs running - that's the angle I was taking before.
In your case, what happens if you prime the pump a couple of times (cycle the key on and off, pausing for 5 seconds when turned on) before ever trying to start it?
If this helps, that indicates a fuel pressure issue, which is often a weak check valve in the pump assembly.
Good luck.