No. Only when you are accepted as a doctoral student at the faculty, you have the confirmation that you meet the requirements to do a doctorate here. Applying for admission as a doctoral student is the first step in being hired as a research assistant through budgetary funds. Admission as a doctoral student is also a prerequisite for enrollment as a doctoral student. Information and forms for acceptance can be found on this homepage under "1. Admission as doctoral student". Please submit all documents to the doctoral office of the faculty in the dean's office, address can be found on the homepage. Here it will be checked, among other things, whether the requirements for a doctorate in the doctoral subject of your choice are met and whether supervision by at least one professor of the faculty is guaranteed. If this is the case, a certificate of acceptance will be issued.
However, accepted doctoral candidates do not necessarily have to be employed at the university. External doctorates are also possible. Employment as a research assistant via budgetary funds should only be made once you have been accepted as a doctoral student. It is handled by the personnel office of the institute or department and goes from there to the personnel department of the central administration. An important document is the doctoral agreement (the form for this can also be found under "1. Admission as a doctoral candidate"), since the time limit of the position is usually based on the start and end of the doctorate as stated in the doctoral agreement.
An exception to this rule is the hiring for externally funded projects, where a decision on a doctorate may only be made at a later point in time. In this case, of course, acceptance as a doctoral candidate can only be applied for once this has been clarified.
Enrollment as a doctoral student takes place via the Student Secretariat and can also take place at any time during the semester. The prerequisite for this is that you have been accepted as a doctoral student at the faculty and can present the acceptance certificate at the time of enrollment. All information about enrollment is available here:https://uni-tuebingen.de/de/920