The very first animal to transform was a rabbit that lived near the river the mad scientist had put his virus in. She hopped out of her burrow unsuspectingly, went down to the river and took an early morning drink from it.
It rapidly started to adjust her body's makeup, and stimulated the pleasure centres of her brain at the same time. She looked at her front paws as the digits separated out into four fingers and an opposable thumb. Her back paws similarly adjusted, though they remained much less dextrous than her front paws. She felt her legs, which constrained tightly so she could bounce herself on them, seem to unclench and allow her to stand taller normally. In fact, she noticed, it seemed like her whole body was growing, and her sense of balance had shifted so she could move bipedally just as easily as quadrupedally.
The changes grew odder still as they continued. Her face seemed to flatten inwards as her snout vanished, her nose and mouth extending from it in a distinctly different way. Her hips had widened and her butt swelled out, and she saw strange mounds of flesh form on her chest as all but two of her nipples vanished and the two that remained started to feel sensitive to the touch.
At last she felt the changes finish. She carefully walked to the river's edge and looked at her reflection, and gasped at what she saw. Other than the soft grey fur that covered her skin, her large ears and fluffy tail, she looked more like a human than a rabbit.
Humans... thinking about that species made her feel strange. Soon it dawned on her that she felt attracted to them. It made sense, she supposed- she had become a creature in between rabbit and human (and, though she didn't know this, her genes had been reconfigured to allow her to mate and produce fertile offspring with either species). As rabbits do, she decided to go try to find something to address her mating desires.
What happened after this would be the start of anthro-rabbits eventually becoming so numerous they threatened to overtake the Earth's human population.