It's not impossible. Significant evidence of the negative will be obtained if performing a thorough investigation (which would be expected to solve the problem if it can be solved) fails to solve the problem.

You could allways argue that we are both not creative / inteligent enough to find a solution and that this is not indicative that a whole society would not find a solution. And this argument may well be correct.

Start with the simpler problem of developing technology as dolphins with hands.

What does that even mean? A dolphin body with functional human arms and a human brain attached and the necessary modifications to make that work? Well now you have got more or less a meremaid with very substantial terrestrial capabilities (well exeeding those of a seal; watch this to get an impression of what I mean ). A group of creatures like that with general knowledge of science might well make it.

Now imagine this creature as strictly waterbound and I think even in this much simpeler problem we can identify a major showstopper: Iron smelting. Imagine this meremaid civilsation with propper hands, and flintstone tools (Can flintstone be found in the oceans? I don't know) and modern scientific knowledge trying to light a fire. They gather mangrooves using their flint axes, build a raft and throw some wood atop to dry. What now? They cannot board the raft to strike or drill fire so they might try to bulid a mirror to use sunlight. Humans did not do that, but they did not know science, so granted. How do they build it without glass or metal? I don't know, but let's say they manage. So now they have fire, not controlled fire, but a bonfire atop a wooden raft. But they don't need a bonfire they need something like a bloomery and then they need to do some very serious smithing only to build something like a very crude excavator arm to do very basic manipulations in a terrestrial environment. And you cannot do smithing under water.

Let's suppose that it's possible to solve this simpler problem ... Can you come up with a particular example of a very simple action that can be performed with hands (underwater, etc.), which doesn't look like it can be reduced to working without hands?

Can you imagine a way a group of quadruplegics ( imho a good aproximation of a stranded dolphin with a human brain - except that their skin does not dry out - ) could fell a tree with stone tools? And delimb it? And bring it to the construction site? And erect it as a pillar?