Although I am not a big fan of them, staffing acuity guidelines do help to set a baseline for staffing, which you can then adjust according to individual patient needs. If you have never used this type of system, it is a computer-based questionnaire that you fill out on each patient, and is designed to provide a rough estimate of the number of hours of patient care required by that patient per shift, for example, a sedated, vented patient requiring frequent suctioning, CPT, blood gasses, use of oxygen monitoring devices, hemodynamic monitoring, multiple IV fluids, central line, receiving 6-8 meds per shift, total care for personal hygiene and positioning with a family requiring extensive emotional support and teaching may come up as 10 hours of care on a 12 hour shift. That patient would be justified as a 1:1.
Another stable post-op patient who has been weaned from oxygen but remains npo with an og tube, IV PCA and orders for ambulation may come up as only 3 hours of care per 12 hour shift. That patient can safely be paired with 1-2 similar patients, as long as your unit is set up so that the nurse has ready access to all 3 of them.
Although your unit is new, your hospital should have some type of system in place for determining acuity and patient assignments on other floors that could be adapted to the PICU. Is there another PICU in your area whose manager might be wiling to help you put such a system into place? (I once managed a small NICU and found the managers of other nearby units to be a wealth of information and assistance.)
Lastly, insist that your hospital provide you with a basic managerial education (at their expense). You should have a basic course on staffing, scheduling, budgets, evaluations, problem-solving, etc. I believe that the lack of basic managerial skills is the downfall of most new nurse managers. Good luck!