Mitcho,
If by 'data', you mean records of universe popping out of our spacetime, then no, there isn't. But there are pretty strong theoretical reasons to believe it can happen. The idea goes like this:
The Uncertainty Principle allows for fields to fluctuate (keep in mind, however, it's your observations that are actually fluctuating - the field doesn't ever have an actual value, instead, it has an egienstate, but taking different observations on it yields different classical values.) between different classical values. For example, an empty vacuum will have a temperature given by T_{dS}=\frac{H}{2 \pi} \sim 10^{-33} eVIf we treat curved spacetime as a gravitational field, the UP should predict fluctuations in spacetime. This should create 'false vacuums', unstable states that are not at a desirable energy level. They would be connected to the background spacetime via a wormhole. However, they should rapidly collapse. But, Guth and Fahri showed that if the inflaton field (the field that drives inflation) managed, via quantum tunneling, to reach a false vacuum, then inflation could occur in this 'baby universe', allowing it to grow to an enormous size. Since wormholes are incredibly unstable, it would quickly collapse, allowing the baby universe to become its own spacetime.
In the past, it seemed that there was very good reason that this could happen. But, I haven't heard too much about it recently, and Sean Carroll ( A cosmologist whose model relies on this 'baby universe' production) expressed his feelings that he is less certain it can actually happen. We really won't know until a proper theory of quantum gravity is fully developed. Trying to apply quantum mechanics by itself to cosmology may be like trying to apply general relativity to particle physics.
The original paper by Guth and Fahri isn't available on the internet, but here are two I managed to find:
The Universe out of a Monopole in a Laboratory?
http://arxiv.org/pdf/gr-qc/0602084v3.pdf
How to Create a Universe
http://philsci-archive.pitt.edu/3196/1/Spec.pdf
