The transporter is the only main one which is absolutely impossible as written. Warp drive is halfway* plausible--not via "subspace", mind you. *(Halfway, in that sublight warp drive is actually plausible. FTL warp drive is ... extremely problematic, if not impossible--reality has built-in causality protection, it seems.)Considering that the normal 'mortal level' tech in Trek already violates currently known laws of physics (for example transporters specifically have 'Heisenberg Compensators' for breaking Uncertainty Principle) I really don't think that this applies.
Speaking of, here's a fun fact: If one could harness the exotic matter required for an IRL warp drive, then one automatically has the starting points of both womrhole creation/stabilization and bigger-on-the-inside spaces all in one neat package, because exotic matter is required for all of them. Takeaway: you could literally see an advanced civilization building a non time-travelling mockup of Peter Capaldi's TARDIS which flies through wormholes and then jumps to STL warp after exiting.