GS305PV3 PoE and Optical Terminal Network ONT PoE

[NG7856]

I have a question that might be crazy but my fiber optic to my house is not near any power supply so I do not know how to power the ONT without new wiring.  I was wondering if I can use a Netgear PoE GS305PV3 to power the ONT.  I found a ONT PoE. 

    Fiber --> ONT (PoE)   -----> ROUTER   ------> PoE Switch ---|

       ^                                                                   |

        | --------------------------------------------------------

Somehow I do not think this will work but I had to ask.

[schumaku]

The PoE switch port (the PSE) can't magically power the ONT PD "through" the router. No tricks, no double bottom.