Allow Wake-on-Lan from internet

Question

I have a network set up behind a firewall router (Cisco ASA 5505). This network has a device, which, to increase its longevity, is allowed to go to S3 or S4 at certain times, but it ought to wake when required, which, in the absence of any other input, would mean a Wake on Lan.

This device has a DHCP address.

The device is only connected to the router / firewall, which will forward all network packets addressed to it. The device ought to be woken from both the internet, and from the local network.

My initial understanding was that any network packet can wake the device, but that is incorrect. I now figure I need the following -

1. Wake on Lan enabled in the target machine BIOS and in the OS (Windows 10) for network device
2. Some way to have the MAC address of this device for the WOL packet
3. Since the device has a dynamic address, some way for the router / firewall to broadcast an incoming internet packet to be broadcast over the ethernet, so it can wake up target device.
4. The router / firewall needs to support 3.

While 1 is simple, others are difficult, if even possible -

EDIT - Another constraint is that the router is not the first in the home network. There could be 1 or 2 levels of redirection before the WOL packet may reach the actual router to which the sleeping device is connected.

If the above is the only way, then -

1. Assuming I cannot "construct" the WOL packet in the router, is it possible to construct this packet from the internet, send it to the router on a specific port, and have the router broadcast it? I am using a Cisco ASA 5505 router. I am not aware of what I should be looking for, from the router, for achieving this.
2. Is there any other, easier way, to achieve this? I cannot change the router to one which can run applications / scripts. I don't have another, always-on machine behind the router which can do this.