is it possible to extend my network using an Airport Time Capsule if the main router is not an apple product?
Yes and No.
Yes, if you connect the Time Capsule to the main router using a permanent wired Ethernet cable connection and locate the Time Capsule where it will be needed to provide additional WiFi coverage, then set up the Time Capsule to provide a WiFi network that uses the exact same wireless network name and password that the main router is using.
No, if you are asking if the Time Capsule can connect to the main router using only a WiFi connection and extend the network in that manner.