Should one specialize in Hadith and Aqeedah, or wait until finishing university, and how, what, and when should one begin?

Firstly, study all the Sharia sciences by taking a sufficient amount from each, starting with the most important then the important, before specializing. There is no objection to combining the sciences of Hadith and Aqeedah (creed); they are both limited sciences. It is preferred to acquire knowledge from scholars (Shuyukh). For benefit in studying Hadith and Aqeedah, you can refer to fatwas numbered: 59736, 126644, 87617. You can benefit from the audio explanations of scholars for texts on creed, such as the explanations of Sheikh Ibn Uthaymeen and Al-Fawzan, and the explanations of Sheikh Salih Al-Sheikh, Al-Barrak, and Al-Khudair, and the explanations of Sheikh Yusuf Al-Ghafais. There is no substitute for reading the books of Sheikh al-Islam Ibn Taymiyyah to understand his methodology, and the books of theaf (pious predecessors) such as: "Al-Radd ala Al-Jahmiyyah wal Zanadiqah" by Imam Ahmad, and "Al-Sunnah" by Abdullah bin Ahmad, and "Al-Radd ala Al-Jahmiyyah" by Al-Darimi, and "Al-Tawhid wa Ithbat Sifat Al-Rabb" by Ibn Khuzaymah, and "Al-Sharia" by Al-Ajurri, and "Al-Iman" by Ibn Mandah, and "Sharh Usul I'tiqad Ahl al-Sunnah wal Jama'ah" by Al-Lalakai, and "Aqidat Al-Salaf wa Ashab Al-Hadith" by Al-Sabuni, and and "Mukhtasar Al-Uluw" by Al-Dhahabi. You can benefit from contemporary academic dissertations by Ahl al-Sunnah. There is no contradiction between university study and seeking religious knowledge; they can be combined.