The goal of this clinical trial is to evaluate the effect of transcutaneous spinal cord stimulation on blood pressure in individuals with an acute spinal cord injury (within 30 days of injury). Blood pressure instability, specifically orthostatic hypotension (a drop in blood pressure when moving lying flat on your back to an upright position), appears early after the injury and often significantly interferes with participation in the critical rehabilitation time period. The main questions it aims to answer are: 1. Can optimal spinal stimulation increase blood pressure and resolve orthostatic symptoms (such as dizziness and nausea) when individuals undergo an orthostatic provocation (a sit-up test)? Optimal stimulation and sham stimulation (which is similar to a placebo treatment) will be compared. 2. What are the various spinal sites and stimulation parameters that can be used to increase and stabilize blood pressure to the normal range of 110-120 mmHg? Participants will undergo orthostatic tests (lying on a bed that starts out flat and then moved into an upright seated position by raising the head of bed by 90° and dropping the base of the bed by 90° from the knee) with optimal and sham stimulation, and their blood pressure measurements will be evaluated and compared.