With systemd, you just need to slightly modify your service to accept preactivated sockets.
You can later use systemd socket activate.
No capabilities, iptables or other tricks are needed.
This is content of relevant systemd files from this example of simple python http server
File httpd-true.service
[Unit]
Description=Httpd true
[Service]
ExecStart=/usr/local/bin/httpd-true
User=subsonic
PrivateTmp=yes
File httpd-true.socket
[Unit]
Description=HTTPD true
[Socket]
ListenStream=80
[Install]
WantedBy=default.target