You can do that by yourself easily. Just write your api and once a week make your app check that endpoint while opening the app. Save the image to the disk of the device then serve your image on the splash screen from the memory of the device.
If you do not want to write your own api, keep some state and persist it. Again once a week check the api you want if there are any new images, if yes download them to your device then serve them.
This is a broad answer for a broad question, but you can achieve what you want with a little bit react(native) and js.