Thanks for your question and it’s great to hear of your interest in biomedical science. You’ve got plenty of time to apply - I’m assuming you’re in Year 12 this year.
I would begin studying for the SAT/ACT in the next few months, get a feel for the test and ideally get it out of the way this year. Colleges generally don’t discriminate against you for taking a standardized test multiple times, so you can always re-take it later in the year or next year if you want to improve your score. Your score will give you a good ballpark indication of which US universities are realistic for you. As an international student, you want to be in the top 50% of the score range (the ranges can be found on university websites).
You’ve also got plenty of time to write the essays, organize the best teacher references, and develop your extracurriculars and leadership activities. For the latter, remember that there is no script nor any particular activities colleges are looking for. The best things show a deep, consistent commitment to things you are passionate about, and that will make you stand out from your peers.
You’re right that you can’t go to medical school immediately in the US. First, you need to study a bachelors degree and gain the pre-medical (or “pre-med”) qualification. This includes many of the science subjects and is closely aligned to neuroscience and biology major requirements. Most of my pre-med friends are majoring in neuroscience or biology. After their 4-year bachelor degree, they will apply for medical school, often at a different university to where they study for their bachelor.
As for other tests - I advise taking two or three subject tests, probably in maths, biology, chemistry or physics, since those align with your interests and are probably your strongest subjects. This will impress admissions officers and help you gain admission to universities at which you can study neuroscience.
Hope that helps, good luck with your studies!