You're right; could is wrong.
will/would/shall/should/: they're not quite right, so I think your can is good.
(Present Simple- I'm not sure. It's still got the word get afterwards, hasn't it? And the getting may still be in the future as the sentence is spoken.)
Anyway, here's another suggestion, "After trying several times we finally managed to get tickets." Now it's all in the past.
Student or Learner