Essentially, no. You have to trust that the app is really doing what it claims to be doing.

If it were open source, would it be different? Maybe. Signal Messenger is open source and the Android build is reproducible. However, the way you reproduce it is to run a Docker image, so that isn't really meaningful unless you audit the code that's used to build it. And then audit the code of the app itself. Fortunately, the Android app is written in Java, so you can easily do static analysis to narrow down what code needs to be audited. Unfortunately, it also includes native code that can reach into arbitrary parts of the heap if it were to try and steal keys. So you'd have to audit all of that. And then keep up with all the changes. Which you aren't going to do.

Even if you did all of that, at some point the naughty thought will occur to you that all your effort can be undone by an operating system update that contains more than it claims to. And then you'll give up.

In practice, it's impossible to really verify anything about how our modern computers work: there are too many people and companies who can silently access key material or just fool us in other ways.

So it's best to understand this work in context - this is not about allowing you to use WhatsApp if your threat model is that WhatsApp is entirely malicious. It's about discouraging governments from going to WhatsApp and saying "you need to give us all your data" because it creates the same situation Apple has: WhatsApp would need to write new software to undo the encryption, and that can be legally argued to be "compelled speech", and thus it can fall outside the legal powers granted under wiretap orders.