Recent experiments in Italy using the Oscillation Project with Emulsion-tracking Apparatus (OPERA) made a bold and controversial claim that possibly, neutrinos exceed the speed of light. This has been subject to debate and mostly ridicule by almost all other astrophysicists as they all stand by and use Einsteins Relativity as basis with all their experiments and current beliefs when it comes to modern universal physics. E=mcsquared. They did certain experiments using neutrinos, capturing them and measuring their speed compared to light going to one place to another with help of GPS satellites above. Certain miscalculations point out and debunk this test however claiming that inconsistencies and VERY slight unbalanced variables such as GPS positioning, transmission of data has compromised said claim thus, we don't really know and so far nothing really still exceeds the speed of light.
When the universe came into being, according to scientific theory, the 'Great Expansion', otherwise known as the 'Big Bang' happened before the physical properties of the universe existed. The Great Expansion took place at many times the speed of light.
Also, realize that when you say 'the speed of light' you are missing out the words 'in a vacuum'. Light travels at different speeds in different media, that's why lenses work.
Also, think of a straight wave approaching a straight shore. If the wave is at an angle to the shore, the speed of the point along the shore where the wave hits the shore can be very fast indeed. In fact, if the wave is parallel to the shore, that point moves much faster than light - in fact, it moves at infinite speed, if it's truly parallel.
velocity is relative. only matter is limited to that speed with something relative but any other theoretical or quantum object can easily travel a giga of that relative velocity to matter, for example look at a star on the west horizon then look at a star on the east horizon. and then just by doing that your point of focus in space just traveled parcepts of space in a matter of seconds.
E=MC2 means that the answer to your question is no. The moment something moved faster than the speed of light it would cease to be anything more than a photon and therefore would no longer be what it originally was so that thing technically never exceeded light speed. But good luck getting anything to go that fast, regardless.