It's analogous to the problem of induction (Hume). Without assumptions, it's impossible to connect past observations to predictions about the future. Observing that the sun rises a thousand mornings does not automatically make it any more or less likely that it will rise tomorrow, unless we make some assumptions, for example that events tend to be similar over time. And those assumptions can't be extracted from the data. Maybe things tended to be similar over time in the past, but that says nothing about the future. The pattern might break tomorrow and to say that it likely won't, is simply an assumption on a higher level.

But it seems like science is "doing fine" despite this problem. Similarly machine learning chugs along fine, because people use their experience and prior knowledge when designing the algorithms. These assumptions are also called inductive biases. They are biasing the learning towards certain patterns (like "things tend to be similar locally").