I've got a Time Capsule (AirPort Time Capsule 802.11ac
, Model Number: A1470
) and had the same problem. Additionally, I also wanted to continue to have automatic Time Machine backups using wireless networking.
Here's my solution if Jaime Santa Cruz's answer doesn't help you.
My Problem
I live in an apartment which includes and provides Internet access only through a wireless access point which isn't under my control. (So, there's no WAN Ethernet cable to connect my Time Capsule to).
I don't have any other Apple wireless devices like an Airport Express. (So the Time Capsule's and Apple's proprietary "Extend a wireless network" feature cannot be used).
I want a simple, inexpensive solution. (So buying an extra wireless router or a Raspberry PI isn't something I want to do).
Solution idea
"Replace the Time Capsule's WAN Ethernet cable with a wireless bridge or WiFi Bridge".
My solution
I found this wireless bridge which I successfully hooked up to my Time Capsule: Vonets VAP11N-300 Wireless Mini WiFi Bridge/Repeater.

Final thoughts
This solution is simple and inexpensive. Time Machine backups from my notebook to the Time Capsule work using the apartment's existing wireless network.
No additional power supply is needed as this wireless bridge can be powered through the Time Capsule's USB port.
The wireless bridge requires a few configuration steps but it's doable.
Using this wireless bridge the Time Capsule is now available on my apartment's wireless network which isn't under my control. (The Time Capsule's wireless access point functionality is turned off).
Alternatively, this solution would also allow to use the Time Capsule as the (private) wireless access point for my apartment and having all devices connect to it ("better security") instead of using the apartment's wireless network. As such the apartment's wireless network would then only provide the (wireless) Internet connection to my Time Capsule and nothing else.