Question: You can't pull a quark out of a hadron, but at time $T = 10^{-43}$ seconds or shortly thereafter, when all particles were created, wouldn't all quarks be individual, and not grouped into hadrons, (which I assume at those energy levels couldn't form)?

Could any of those stand alone quarks still be by themselves today?

Answer: 
As Wikipedia says, the physics during the [Planck epoch](https://en.wikipedia.org/wiki/Chronology_of_the_universe#Planck_epoch) is not well understood. But we can say that the density of matter (and of energy) at that time was *extremely* high. It's not like there were isolated free quarks floating around in space. They were all packed *very* tightly together in the quark-gluon plasma.

Once the temperature fell sufficiently for hadrons to exist, the quark-gluon plasma "froze", which rapidly confined the quarks into hadrons. There could not be any stand-alone quarks that somehow managed to remain free.
No, due to a phenomenon known as color confinement, quarks are never directly observed or found in isolation; they can be found only within hadrons. There is an [article](https://en.wikipedia.org/wiki/Color_confinement) about this on Wikipedia.