Yes just climb the calcite rift, that looks too tight, follow the calcite up, when it levels off carry on up through the slot above, don't go straight ahead. Surprised it did not look muddy as I think that's the route everyone uses.
The rift climb is not that tight or hard, never bothered rigging the pitch once up there as there is no need really, I mean if you think the rift climb it is hard, you won't like the rest of the cave beyond the 20m down pitch. Lots of squeezes and much more awkward (though shorter) rift climbs + lots more mud. The full trip is definitely NFTFH especially if you are brining the ropes to rig the drops into Notts 2.