Hello Hanna,
Less than a year of asana practice and in what style please? What is your general condition, age, fitness and activity level?
You’ve mentioned your hamstrings are not at issue. Please, what are you using to make this determination?
Is this pose you are working on Dandasana or is Danda used as a beginning position to enter Paschimotanasana?
The ability for students to bend forward - with integrity - is facilitated by mobility in the pelvis. There are those things which affect the pelvic orientation in the front body and similar fellows in the back body. The “rounding” of the spine occurs in the thoracic spine which is already innately curved in that direction. For many, the issue is the hamstrings and the quadratus lumborum, a muscle in the lower back. However muscles work in synergies so isolating one is rarely accurate or effective.
The purpose of a folded blanket or pad under your sitting bones - not a block please as it does not provide the landscape or stability for this - is to tip the pelvis forward (or anteriorly, as my lovable, but narcissistic, anatomy chums would write). That tip is and should be the genesis for forward bending.
If the student feels as though they will “shake like they are going to explode” it seems like an intervention on the part of the teacher is more than warranted. Perhaps you do not take enough height. More likely though is that you haven’t (yet) cultivated in your body that which is needed for Paschimotanasana. It’s no crime but such a student should be guided toward other work so that the proper actions can be nurtured.
Finally, if you are an anxious person understand that there is a certain nature of surrender in forward bending poses and that might be a catalyst for a great deal of resistance on your part. That resistance can manifest itself in the mind and the body in a myriad of ways. Ergo it is best to find the joy of light in the yoga clothing you choose, place your mat near the front of the class, and emerge from the shrubbery enough to engage in dialogue with your teacher
If that is not fruitful then perhaps it’s time to mine a different jewel.