but we can not do experiments to scientifically prove an event.
You cannot "prove" anything is science. We build evidence to support a theory. The evidence may become overwhelmingly supportive of the theory, but the theory is never "proved", simply exceptionally well-supported.
How does one do a scientific experiment on an event that is postulated in history.
By working out what evidence such an event would leave, and then looking for that evidence. If Big Bang cosmology is true, then there should be a relic radiation permeating the Universe consisting of the first photons to fly free from the early dense ionised gases that ould have trapped photons. Thsi radiation should be black body in spectrum, and it should be very low temperature - just a few degrees Kelvin - owing to the expansion of the Universe since the photons escaped the dense gas.
Guess what? We see the Cosmic Microwave Background Radiation, exactly as it should be if it is the hypothesised radiation from the time following the Big Bang. The CMBR is excellent evidence for the Big Bang comsology, despite the fact that these photons were emitted 13.6 billion years ago.
Compared to the above, finding evidence for the creation event of the Universe that happened just 6000 years ago should be a piece of cake.
Now, what evidence should we expect from this creation event?