So congrats on nursing school
and best of luck on surviving an accelerated program. I myself recently graduated a 12 month 2nd Degree BSN from a top school and I know how tough it will be for you. I'm an older murse at 50 hence the name and originally thought I wanted ER also but fell in love with ICU and happened to land an ICU job after school. Let me first address what I've seen that made nurses successful in landing that first job in an ICU vs. having to do a tour of medsurg first. Then I will also hopefully clear up or solidify some of your perceptions of what it means to be in the ICU especially as a new grad.
First and most important thing I saw in new nurses in landing an ICU role or even getting an interview was getting relevant experience during nursing school. Ideally you will do a clinical in an ICU you would love to work or even be willing to work in during your final rotation. If you can land this go straight to the charge nurse professionally introduce yourself and make it clear that this is where you would love to work. Work your ass off and at an appropriate time ask the charge nurse if they would introduce you to the director for a short meeting and make your pitch to them on your interest. Don't beat around. This is the #1 way I saw new grads get into an ICU even if the ICU didn't hire new grads.
#2 Start looking now at hospitals you would like to work in that specifically have new grad programs that will hire into the ICU. Find out the process to apply, be ready to apply when possible and do everything you can to stand out. Be willing to relocate. Network if you can with current employees there or anyone you can get a relationship with.
#3 Last and probably least realistic route is to apply for ICU jobs/programs that will accept new nurses but are not exclusively new nurse. Unless you are the top of your class from a great name school its a tough route as they literally have hundreds of applicants including from experience med surge nurses that they already know in their system.
As a backup if all the above fails find the hospital you want to work for and get in med surge and do your time going route #3 above. Depending on your market despite the so called shortage landing a GOOD new nurse job can be tough as any hospital needs to make a SIGNFICANT investment in training you and then hopes you will stay. Those that have extensive new nurse training programs that focus on ICU tells you also a lot about the hospital ... potentially.
It's not clear from your post that you have spent significant time in the trauma ICU. Don't take this as a lecture I just want you understand it a little better at least as I have experienced both. It's not the ER. If you know this just ignore everything else I have to say. In fact if you haven't discovered ER Nurses and ICU Nurses have a 'friendly' rivalry. ER nurses think ICU nurses just fluff pillows and ICU nurses wonder if ER nurses have ever heard of a patient history or realize they have names.
Patients arrive stable generally from the ER or a rapid response but can go downhill real fast. You spend your time monitoring and looking for trends and trying to head off disaster. Doctors actually spend very little time with them you are the primary health care advocate. You will take complete care of them even if you have CNA's who will at best assist. You really need to enjoy pathology and physiology your cases will be complicated. You will be the go to person for the family and will get to know them and the patient and despite the best efforts of all quite a few will die as a normal part of business. If they code in an ICU even if they recover they most likely won't next time or their long term quality of life will not be great. This can be emotionally hard. ICU nurses tend to have the highest burnout especially PICU.
Time management. You will have 2 hope to god not 3 patients and it's not easier in an ICU compared to the ER or MedSurge it's just different. You will chart ... and chart ... and chart ... and in between you will give bed baths maybe several times a day (ICU patients don't ambulate to the bathroom) ... you will give meds ... you will give blood ... you will do doctor notifications ... you will take patients for scans ...you will chart ... you will wonder why you have a headache and realize you haven't had a drink, bite to eat or bathroom break in 8 hours.
If you are younger and a new grad you might have some resentment that you haven't paid your dues but more likely it will be they will wonder if you have enough life experience never mind nursing experience. It takes at least a year or two even for experienced nurses to come up to speed never mind a new grad in the ICU. As the ICU nurse you are the expert and you must be assertive and balance all the family, doctors and various other ego's even more so than any other area. Hard to do as both young and new and without looking foolish or arrogant. Dumbest thing I said to my preceptor was how do you call a rapid response ... rolled her eyes at me and laughed ... you are the rapid response if you need help yell real loud.
If all that hasn't scared you off congrat's I LOVE the ICU and it is a calling and best of luck. I personally don't think spending time seasoning in a med surge is necessary if you have what it takes to work in the ICU. Others may differ.