What can I do to earn my qualifications to work in ICU? I have more than 3 years MED SURG experience; but, my ultimate goal is to work in ICU. How can I make the transition to ICU?

Apply to the unit. Get into a residency. They will train you. Make sure you have had good evals and recommendations from your current Manager. You can do anything you set yourself to do. DO IT!!!!!

I'll be honest, I haven't read other's reply so if there's an overlap, its great :) with that being said, here's my story, abridged version.

In my hospital, I went from medsurge (tele/geriatric/vent/infection disease/psych) unit to ICU. The same manager that I had there, though she end up going to ICU, I 'kind of' followed her ... She had to interview me for ICU position, mind you, she KNEW me already, and asked me one question, that stood out "What have I done up until that point to improve my skills and knowledge?"

I've been in the same hospital for the last 9 years, 7+ of which were on on med-surge unit. I've NEARLY ALWAYS took an opportunity to float, because wanted to learn more stuff, get to know other people, etc.

I've also been on the journey of getting certified. At first, it was CSMRN vs BC. But after some reading and talking with other people, I learned about CCRN. This was 2018. So when my ex/future manager asked me what have I done to improve my self:
I did on my own Laura Gasparus CCRN review course, I went cover to cover PCCN book (and not skimming but actually writing out crazy amount of notes), I did medsurge certification review course and another PCCN/CCRN review course through CE Direct (https://cedirect.continuingeducation.com), I went through Mark Klimek NCLEX review (https://klimekreviews.com), also did an ECCO class through AACN. On top of that, I took every opportunity, even if it wasn't my turn, to float to other units. During 2020-2021, I spend more then half of my time in PCU. My hospital opened PCU for the first time during that period...
Finally, when I got into ICU, like Socrates said - I know that I know nothing - as much as I thought I was familiar with, I was lucky that I had a decent foundation, but in ICU setting felt like a lost poppy lol.
Besides the whole union/seniority thing, I strongly believe that the main reason why I was able to take on this opportunity and not drown (notice I didn't say succeed) was because over the last 5 years, I've invested HUNDREDs of hours into self education and building up my foundation. I also took on challenges of precepting new hires and working with nursing students - the questions that I'd get were challenging and to answer them, one really has to be comfortable with the topic.

Besides applying for the ICU positions and showing your determination, if you haven't yet, look into certification. If you current position allows, explore the option of PCCN ~ those who know and understand what this board exam is about, they are likely to appreciate the dedication from the perspective employee.

Good Luck

Education: ACLS & PALS are most often required. Your facility might offer them for employees even if not needed for your position; on your own each cost around $250. TNCC (trauma nursing core course) is an exceptional resource for knowledge and critical thinking; and ABLS (advanced burn life support) great education.
CE courses with specific critical nursing themes (chest tubes, AFib, Stroke, etc.) - CE Central has a large collection of FREE (certified and accepted in all states) classes.
Ask your hospital or other sites (university and magnet hospitals most often have extras), where you'd like to start what do they offer: internships? volunteering? prep programs? precepted positions? "Level I clinician"- entry level position to train on the job, etc.
Where are you located? Where would you relocate for an opportunity? What is your level of education? A BSN would open many doors.
There's a CE class on CE CENTRAL now to prepare for CCRN exam (critical care RN). If you can obtain this certification, any ICU would work with you to add you to their team. It costs #300, study at your pace for 6 months. If you cannot take the exam ("You must also meet the clinical practice requirement of 432 hours in direct care of acutely/critically ill patients, with 144 of those hours accrued in the 12-month period prior to your scheduled renewal date."), proof of taking this course will open the arms of your employer - showing you are determined to step into this specialty. Then you can take the exam after working 144 hours even if you're level I clinician, and probably advance to higher level clinician.
It's easy when you're passionate about it, doors open, and you're guided. There's much need for nurses everywhere, but the advanced-care positions require people who are committed to constant growth, development, and self-improvement.

Maybe at 5 years Med surg, look for a hospital that has an ICU preceptor ship that you can work on and then transition. you want that preceptor ship

Have you asked your hospital (wherever you are working now) to transfer to ICU, or applied for an ICU position? I'm sure they would love to have you as is. I know several nurse interns that actually started straight off in the ICU, training. Usually the only true obstacle is letting ICU know you want to be there because they will usually bend over backwards to make it happen.