For what concerns Galileo, there is some discussion. Some say he actually performed the experiment somewhere between 1589 and 1592 in Pisa, others say it was only a thought experiment.

But there´s evidence he was not the first to carry out the experiment.
In 1586, so at least 3 years prior to Galileo, Simon Stevin and Jan Cornets De Groot performed the experiment in Delft.

Were they the first to design it? Maybe, maybe not. Around that time several people were looking at the then accepted theories with a critical eye...