is there a way to create online php server without port forwarding and having to edit my router settings? I want to create a google maps tracking server and update it remotely. I already have its php code.
That depends on quite a few factors.
If you have a website online, then obviously yes, you can. There are free and cheap webhosting providers that could do this. You upload your code to that site, and using an url you get to the code.
If you want to do everything from home, then it becomes a completely different story.
Do you have a router? If so, then no, you really need to configure your router in order for it to know where the traffic needs to go.
If you really don't want to configure your router, you could connect that pc directly to the modem, and no portforwarding would be necessary. Of course, that means that only one pc has internet access.
There really is no other way, and that is due to what a router does.
You basically go from 1 public IP to many private IP's. Your webserver is behind one of the many private IP's, and when someone opens your website through the public IP, the router then needs to forward the traffic to your webserver. It can only do that by adding a port forwarder in the router. Otherwise it simply doesn't know where the traffic needs to go.