Hypothetically you could install malware hidden in what you thought was an innocent app, and that malware could download images. Or the malware could install other malware that downloaded images. The second is easier to imagine with an old version of Android, where there was a global setting to allow installation from unknown sources. Either way this assumes that the owner of the phone downloaded an app from a dodgy source and that app turned out to be infected, because that's how most malware infections happen.
However I've never heard of malware that downloads indecent images. Technically possible, but I've never heard of such a thing.
It is possible for someone who is able to log into your Google account to remotely install an app to your phone, but as has been said you will get a notification. The phone's owner would still need to open the app though: an app installed that way can't run without someone actually opening it at least once.
A quick search of the Play Store found that there are apps that look like calculators but can be used to hide images (e.g.
Calculator - Hide Photo, Video - Apps on Google Play). However I see nothing in that app's description that says it can download images, it just talks about hiding images that you have downloaded. So if it was that app it would not explain how the images were downloaded (the purpose of that app is to allow the user to hide images they don't want others to know they have).
I hate to say this, but people are secretive about things that they find shameful or are illegal. That is a simpler explanation, even though you don't believe it. Of course I know nothing of the circumstances, even what country you are in, so I'm not making an accusation. But "the phone was infected with malware that installs images so indecent that the IP address of the source is being monitored" seem less likely than any of "the person has an enemy who had access to their phone", "someone else doesn't want to use their own phone for this", "the police are framing the person" or "the person has been keeping a secret from their family". It might be that you are right, but it seems a long shot (unless they were aiming to frame a specific individual why would anyone even write such an app?).
