If your public IP from your ISP is 12.13.14.15, and your internal block is 192.168.0.0/24, then your ISP can send a packet to 12.13.14.15 destined for 192.168.0.7, and without a firewall your router will happily forward it. An attacker who can convince intervening routers to send traffic destined for 192.168.0.7 to 12.13.14.15 (and these attacks do exist, particularly over UDP) can also do that.

Send packets to the device? A NAT is in it's most basic form a mapping from one IP/port set to another IP/port set describable by some function "f" and its inverse "g". The common home user case has the firewall detect a flow from inside the network and modify "f" and "g" to allow this flow. Without the firewall, and assuming you want your devices to talk to the internet in some way, the NAT would forward (with modifications) traffic based on "f" and "g" to all your devices.