Are there experiments in which scientists can recreate aspects of the Big Bang?
I think that the operation of particle accelerators such as the Large Hadron Collider at CERN can be seen as one of these experiemnts.
Basically what they do in these experiments is what we do when we are kids: we break things to "see" what is inside!
They break particles to detect smaller components that in turn may be broken again and again and from the observation of these "debris" the Physicists can understand what the situation was at the start of the universe.
Exactly like a toy, we break it into the component pieces so that we can say: "at the start my toy was a set of given bit and pieces"...in the same way the Physicists can say: "at the moment of the Big Bang there were these elementary components (obtained breaking bigger stuff) that in time came to form bigger objects such as electrons, protons etc."
Every time they break a small particle they "go back in time" discovering more ancient bits and pieces (as close as possible to the instant of the Big Bang).
Hope it helps!
We cannot reproduce any of the conditions of the "Big Bang" until quite some time after it occurred, because we don't even know what the truly "fundamental" forces or particles were at that time. Even our plasmas and quarks had to come FROM the "Big Bang". So we can theoretically and maybe mathematically imagine consistent conditions, but there is no way we can experimentally recreate them.