Kdtyjb

I am third-year bachelor student currently seeking a research internship in Germany and I encounter many group websites that say something like: “We have positions for bachelor projects.” I am wondering whether this means that these projects are only intended for a thesis and suitable for final-year students about to graduate, or do they also welcome not-final-year undergrad students? (BTW, my discipline is physics, and I am not looking for position in my home institution).

I guess it’s gonna look stupid if I send an inquiry to the professor without figuring out this problem.

In most cases professors will not be offended if an eager, and knowledgeable, undergraduate approaches them about working on a project. This doesn't mean they will have a position for you, but it does mean it is always worth asking. Reading their website and seeing what they are interested in is a great start.

From my experience in German academia (CS/Math), "We have positions for bachelor projects" means just that. Final year students (of that department!) who want to do their bachelor thesis can write to the professor and get a project. Departments are usually obligated to offer several of these projects, so that every student of the department can have a shot at writing a bachelor thesis.

This notice is in my experience addressed to students of the department and does not imply anything about 'research internships' (My experience meaning, on our webpage we have a similar sentence and this is exactly what it means). From your question is it not clear to me if you are already a student of said university, this might be quite important here.

However, the professor might still be interested in offering a project to you (as discussed in Astronome's answer), unrelated to their bachelor projects, so just write a polite email and ask him.

If bachelor theses are a thing in your programme, the statement in question almost certainly is about thesis projects.

However, at least in my experience, most research produces side projects all the time, and a group may just have one that fits your requirements and abilities.
If a group advertises specific projects and does not find a bachelor student, they may also be happy if you are willing to take on such a project (if you bring all the prerequisites).

A very crucial factor in this is whether they expect that your work is worth the resources they invest into you (probably mainly supervision time).
For example, my personal, field-dependent rule of thumb is that the average bachelor project takes as much time to supervise as to do the respective work myself.
Compared to this, you have the advantage that you do not need to supervision for writing and defending a thesis, however, you also have the disadvantage that there is less incentive to make you finish your project.
Another factor playing into this is the kind of work you would do:
Experimental projects tend to require more supervision that theoretical or computational ones, shifting the balance against you.

Thus, the most crucial aspect is that you can convince them that you are capable and willing to complete a small project with a certain degree of independence.
Enthusiasm about what the group in question is actually researching certainly helps in that respect.

It is definitely not bad to show initiative yourself but you have to motivate why you want to gain internship in the particular lab or topic :). You should also be ready to provide recommendations from your lecturers or Professors.

Also, a very good way in getting internship places is to ask your study advisor for help, or contact professors that you had lectures at. It is much easier to get a place when someone with more experience is guiding you. Moreover, you shall ask at your faculty if it is possible to get a student job, it very often includes some research, practical work for the chair.

In any way, you shall be ready to send some e-mails around with your CV and a good motivational letter. I got a post-bachelor internship in Berlin after 20-30 e-mails sent, which is considered pretty quick for a foreigner who does not speak German :). In general, scientific labs like free/cheap voluntary working force, so it should be quite possible to get a place for internship. Good luck!