No. If you apply now, then you will not be able to start building a credit history. Instead, you will just be building a history of applying, which is even worse than having no history.
Student credit cards are almost never given to anyone under 21 who has no credit history. Most companies haven't issued even credit card to anyone under 21 without a full time job in about 10 years. Applying for a student card when are 19 and have no credit history and no full time job is basically asking them to deny you.
To have any chance of getting to build a credit history, ever, the most important thing right now is that you do not apply, so that you will have a history of not applying and might be able to get one when you are 21 or have a full time job -- if that is the very first time in your life that you apply.