Is it typical for STEM students to be responsible for coming up with their own thesis projects? I'm a first year recent science/STEM international PhD student. My advisor has mentioned to me that it is my responsibility  to come up with a project all on my own. I believe the understanding is that I come up with a project and only will receive help when I'm stuck. I'm wondering whether this is normal? I've asked every student in my cohort how they came up with their project and they said it was a mutual thing between them and their advisor. They both sat down and bounced ideas around or their advisor had a grant and they are taking a sub-portion of the grant idea and they will later on in their fourth/fifth years add more to it on their own merits. 

I'm very worried about this, because I was always under the notion that in graduate school you receive guidance from your advisor is what projects might work from their experience. Later, at the post-doc level, the person is experienced enough to master their own project from scratch. 

I'm in an unfunded lab and don't have access to protocols/money for wet lab. I have come up with multiple ideas, but they don't seem promising. My advisor only liked one of the ideas, however she is not sure that it will work. I spoke with other professors and they don't think my previous ideas will lead anywhere. 

There are two other PhD students in my lab. They have not taken their quals yet and are in their fourth years. I'm worried about my future outlook since my advisor has not had a graduated PhD student yet. We are her first ones. 

What is my best course of action?

Thank you in advance.
I would say it is not typical to expect a student to come up with their project completely on their own, although I will admit that I have done this with one particular PhD student who had already demonstrated in his master's project that he was sufficiently capable that it made sense to let him "drive" the project so long as it was something I felt comfortable advising. This was also possible because he had a secure source of funding that allowed us to do this.

However, for a typical student, such a route would be very risky and quite prone to failure, especially if she is just beginning her graduate work. I would not expect the student to be able to come up with independent ideas for a project until well into the course of the PhD program.