[MAIN SPOILERS]I think it's pretty obvious now how Jon will get beyond the wall..

After this episode where everyone on team Dany seem to not fully believe Jon aside from Tyrion, and that Jon needs the full support from Dany means he needs her dragons too, he will realize the only thing that will make them 100% believe him is if they SEE the white walkers themselves, so he will decide to go beyond the wall and try and bring one of them to Dany.

Bonus: I think he will make this decision at dragonstone when Jorah is there and this is how Jorah will end up coming with Jon beyond the wall :)