I would say it is extremely difficult to break into the PE space as a new management team right now, particularly if your entire team has no track record. There are quite a few good to very good teams out there either looking for assets with backing from existing PE shops or looking for funding from a PE shop. If you're going to break in, it is probably through someone like Carnelian or Post Oak.
You'll need line of sight to an existing asset, probably paying PDP at a high discount and paying nothing for upside (but it needs to have upside). You're also going to need a pretty robust business plan for running an operating company.
The days of PE management teams are sort of drying up, although there has been a bit of resurgence recently. For a while, the market was heading towards the PE shops trying to internalize a lot of the management team functions. That's what I've been seeing anyway.