Does Galileo's thought experiment suggest that we can not ever check if absolute space exists?

In particular I am talking about Galileo's thought experiment of the ship. In my understanding of the experiment, we can not ever check absolute motion (which I guess would be motion in absolute space) of an object, and that we can only probe into reality with respect to a reference frame.

I am guessing similar thoughts could have entered Newton's mind who was born seventy eight years after Galileo, but then I wonder, why he suggested a concept such as absolute space existing (1). As for me it seems like a Russels Tea cup type scenario where we are talking about something whose existence can not be refuted or not, as a result then, unscientific.

Surely, I must be missing something here, could someone give me a prespective why absolute space would nonetheless be a nice idea even if we can't verify it's existence? Or maybe if I am completely wrong in understanding till now, how can we indeed verify it?

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1: https://en.wikipedia.org/wiki/Absolute_space_and_time